Mixing
Is there a shorthand for signifying that the numerator/denominator hasn't changed?
$begingroup$
Sometimes, when I'm solving problems in school, the numerator or the denominator will stay the same throughout multiple steps as I solve the other. This gets very tedious, and I was wondering if there was a shorthand or symbol I can use to show that it stays the same.
What I'm looking for:
$$frac{(x+3)(x+5)}{x+2}$$
Instead of: $$frac{x^2+8x+15}{x+2}$$
I can use: $$frac{x^2+8x+15}{beta}$$ or some other symbol.
notation
asked Jan 7 at 23:59
Moeez MuhammadMoeez Muhammad
132
$endgroup$
add a comment |
$begingroup$
Sometimes, when I'm solving problems in school, the numerator or the denominator will stay the same throughout multiple steps as I solve the other. This gets very tedious, and I was wondering if there was a shorthand or symbol I can use to show that it stays the same.
What I'm looking for:
$$frac{(x+3)(x+5)}{x+2}$$
Instead of: $$frac{x^2+8x+15}{x+2}$$
I can use: $$frac{x^2+8x+15}{beta}$$ or some other symbol.
notation
asked Jan 7 at 23:59
Moeez MuhammadMoeez Muhammad
132
$endgroup$
2
$begingroup$
If you say that this what you mean you can do it if you explain yourself. You can do anything you want if you explain yourself. Or if you are really going to go a long time factoring the numerator just say "Let's concentrate on the numerater. $(x+3)(x+5) = x^2 + 8x + 15$ and ...."
$endgroup$
– fleablood
Jan 8 at 0:02
$begingroup$
Hi Moeez, generally using a variable as you have is to indicate a constant value. Here as $beta$ is replacing an expression of another variable $x$, it is generally better (for clarity to the reader) to write is as such, i.e. $beta(x)$. There is nothing wrong with this practice as well, in fact, I would encourage it whenever it makes the expression you are working with simpler to interpret.
$endgroup$
– DavidG
Jan 8 at 4:35
add a comment |
$begingroup$
Sometimes, when I'm solving problems in school, the numerator or the denominator will stay the same throughout multiple steps as I solve the other. This gets very tedious, and I was wondering if there was a shorthand or symbol I can use to show that it stays the same.
What I'm looking for:
$$frac{(x+3)(x+5)}{x+2}$$
Instead of: $$frac{x^2+8x+15}{x+2}$$
I can use: $$frac{x^2+8x+15}{beta}$$ or some other symbol.
notation
asked Jan 7 at 23:59
Moeez MuhammadMoeez Muhammad
132
$endgroup$
Sometimes, when I'm solving problems in school, the numerator or the denominator will stay the same throughout multiple steps as I solve the other. This gets very tedious, and I was wondering if there was a shorthand or symbol I can use to show that it stays the same.
What I'm looking for:
$$frac{(x+3)(x+5)}{x+2}$$
Instead of: $$frac{x^2+8x+15}{x+2}$$
I can use: $$frac{x^2+8x+15}{beta}$$ or some other symbol.
notation
notation
asked Jan 7 at 23:59
Moeez MuhammadMoeez Muhammad
132
asked Jan 7 at 23:59
Moeez MuhammadMoeez Muhammad
132
asked Jan 7 at 23:59
Moeez MuhammadMoeez Muhammad
132
asked Jan 7 at 23:59
Moeez MuhammadMoeez Muhammad
132
asked Jan 7 at 23:59
Moeez MuhammadMoeez Muhammad
132
132
2
$begingroup$
If you say that this what you mean you can do it if you explain yourself. You can do anything you want if you explain yourself. Or if you are really going to go a long time factoring the numerator just say "Let's concentrate on the numerater. $(x+3)(x+5) = x^2 + 8x + 15$ and ...."
$endgroup$
– fleablood
Jan 8 at 0:02
$begingroup$
Hi Moeez, generally using a variable as you have is to indicate a constant value. Here as $beta$ is replacing an expression of another variable $x$, it is generally better (for clarity to the reader) to write is as such, i.e. $beta(x)$. There is nothing wrong with this practice as well, in fact, I would encourage it whenever it makes the expression you are working with simpler to interpret.
$endgroup$
– DavidG
Jan 8 at 4:35
add a comment |
2
$begingroup$
If you say that this what you mean you can do it if you explain yourself. You can do anything you want if you explain yourself. Or if you are really going to go a long time factoring the numerator just say "Let's concentrate on the numerater. $(x+3)(x+5) = x^2 + 8x + 15$ and ...."
$endgroup$
– fleablood
Jan 8 at 0:02
$begingroup$
Hi Moeez, generally using a variable as you have is to indicate a constant value. Here as $beta$ is replacing an expression of another variable $x$, it is generally better (for clarity to the reader) to write is as such, i.e. $beta(x)$. There is nothing wrong with this practice as well, in fact, I would encourage it whenever it makes the expression you are working with simpler to interpret.
$endgroup$
– DavidG
Jan 8 at 4:35
2
2
$begingroup$
If you say that this what you mean you can do it if you explain yourself. You can do anything you want if you explain yourself. Or if you are really going to go a long time factoring the numerator just say "Let's concentrate on the numerater. $(x+3)(x+5) = x^2 + 8x + 15$ and ...."
$endgroup$
– fleablood
Jan 8 at 0:02
$begingroup$
If you say that this what you mean you can do it if you explain yourself. You can do anything you want if you explain yourself. Or if you are really going to go a long time factoring the numerator just say "Let's concentrate on the numerater. $(x+3)(x+5) = x^2 + 8x + 15$ and ...."
$endgroup$
– fleablood
Jan 8 at 0:02
$begingroup$
Hi Moeez, generally using a variable as you have is to indicate a constant value. Here as $beta$ is replacing an expression of another variable $x$, it is generally better (for clarity to the reader) to write is as such, i.e. $beta(x)$. There is nothing wrong with this practice as well, in fact, I would encourage it whenever it makes the expression you are working with simpler to interpret.
$endgroup$
– DavidG
Jan 8 at 4:35
$begingroup$
Hi Moeez, generally using a variable as you have is to indicate a constant value. Here as $beta$ is replacing an expression of another variable $x$, it is generally better (for clarity to the reader) to write is as such, i.e. $beta(x)$. There is nothing wrong with this practice as well, in fact, I would encourage it whenever it makes the expression you are working with simpler to interpret.
$endgroup$
– DavidG
Jan 8 at 4:35
add a comment |
1 Answer
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$begingroup$
Sure, you can let $beta = x+2$.
There is nothing mathematically incorrect about letting another variable be equal to another variable/expression or substituted for it (though it can result in some nuances to be aware of, for example in integration/calculus). Sometimes it can even be more convenient - not so much in this case, but if you're dealing with larger, more complicated expressions, it can certainly make the work easier.
The key point would be to make sure it's clearly declared that $beta = x+2$, though, or whatever you're substituting it for, so that there's no ambiguity with the reader.
EDIT: As noted in the comments, however, for this context specifically as $x$ is a variable, it is more appropriate to let $beta$ be $beta(x)$ in the above discussion. If there was no variable - for example, it was $pi + 3$ where $pi$ denotes the usual constant, you could just have $beta$. Though in practice it's highly unlikely anyone will be confused either way.
answered Jan 8 at 0:01
Eevee TrainerEevee Trainer
5,8011936
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add a comment |
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1 Answer
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$begingroup$
Sure, you can let $beta = x+2$.
There is nothing mathematically incorrect about letting another variable be equal to another variable/expression or substituted for it (though it can result in some nuances to be aware of, for example in integration/calculus). Sometimes it can even be more convenient - not so much in this case, but if you're dealing with larger, more complicated expressions, it can certainly make the work easier.
The key point would be to make sure it's clearly declared that $beta = x+2$, though, or whatever you're substituting it for, so that there's no ambiguity with the reader.
EDIT: As noted in the comments, however, for this context specifically as $x$ is a variable, it is more appropriate to let $beta$ be $beta(x)$ in the above discussion. If there was no variable - for example, it was $pi + 3$ where $pi$ denotes the usual constant, you could just have $beta$. Though in practice it's highly unlikely anyone will be confused either way.
answered Jan 8 at 0:01
Eevee TrainerEevee Trainer
5,8011936
$endgroup$
add a comment |
$begingroup$
Sure, you can let $beta = x+2$.
There is nothing mathematically incorrect about letting another variable be equal to another variable/expression or substituted for it (though it can result in some nuances to be aware of, for example in integration/calculus). Sometimes it can even be more convenient - not so much in this case, but if you're dealing with larger, more complicated expressions, it can certainly make the work easier.
The key point would be to make sure it's clearly declared that $beta = x+2$, though, or whatever you're substituting it for, so that there's no ambiguity with the reader.
EDIT: As noted in the comments, however, for this context specifically as $x$ is a variable, it is more appropriate to let $beta$ be $beta(x)$ in the above discussion. If there was no variable - for example, it was $pi + 3$ where $pi$ denotes the usual constant, you could just have $beta$. Though in practice it's highly unlikely anyone will be confused either way.
answered Jan 8 at 0:01
Eevee TrainerEevee Trainer
5,8011936
$endgroup$
add a comment |
$begingroup$
Sure, you can let $beta = x+2$.
There is nothing mathematically incorrect about letting another variable be equal to another variable/expression or substituted for it (though it can result in some nuances to be aware of, for example in integration/calculus). Sometimes it can even be more convenient - not so much in this case, but if you're dealing with larger, more complicated expressions, it can certainly make the work easier.
The key point would be to make sure it's clearly declared that $beta = x+2$, though, or whatever you're substituting it for, so that there's no ambiguity with the reader.
EDIT: As noted in the comments, however, for this context specifically as $x$ is a variable, it is more appropriate to let $beta$ be $beta(x)$ in the above discussion. If there was no variable - for example, it was $pi + 3$ where $pi$ denotes the usual constant, you could just have $beta$. Though in practice it's highly unlikely anyone will be confused either way.
answered Jan 8 at 0:01
Eevee TrainerEevee Trainer
5,8011936
$endgroup$
Sure, you can let $beta = x+2$.
There is nothing mathematically incorrect about letting another variable be equal to another variable/expression or substituted for it (though it can result in some nuances to be aware of, for example in integration/calculus). Sometimes it can even be more convenient - not so much in this case, but if you're dealing with larger, more complicated expressions, it can certainly make the work easier.
The key point would be to make sure it's clearly declared that $beta = x+2$, though, or whatever you're substituting it for, so that there's no ambiguity with the reader.
EDIT: As noted in the comments, however, for this context specifically as $x$ is a variable, it is more appropriate to let $beta$ be $beta(x)$ in the above discussion. If there was no variable - for example, it was $pi + 3$ where $pi$ denotes the usual constant, you could just have $beta$. Though in practice it's highly unlikely anyone will be confused either way.
answered Jan 8 at 0:01
Eevee TrainerEevee Trainer
5,8011936
edited Jan 8 at 6:08
answered Jan 8 at 0:01
Eevee TrainerEevee Trainer
5,8011936
answered Jan 8 at 0:01
Eevee TrainerEevee Trainer
5,8011936
answered Jan 8 at 0:01
Eevee TrainerEevee Trainer
5,8011936
5,8011936
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$begingroup$
If you say that this what you mean you can do it if you explain yourself. You can do anything you want if you explain yourself. Or if you are really going to go a long time factoring the numerator just say "Let's concentrate on the numerater. $(x+3)(x+5) = x^2 + 8x + 15$ and ...."
$endgroup$
– fleablood
Jan 8 at 0:02
$begingroup$
Hi Moeez, generally using a variable as you have is to indicate a constant value. Here as $beta$ is replacing an expression of another variable $x$, it is generally better (for clarity to the reader) to write is as such, i.e. $beta(x)$. There is nothing wrong with this practice as well, in fact, I would encourage it whenever it makes the expression you are working with simpler to interpret.
$endgroup$
– DavidG
Jan 8 at 4:35