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I appreciate anyone taking a look at this.

It's been ages since I've been in algebra/calculus and need to figure out if $\dfrac {(x-y)}{x}$ can be simplified or would it be $\left(1 - \dfrac yx\right)$?

Thank you,


Thanks to all the very speedy responses. I guess my algebra isn't as rusty as I thought. This question can be marked as solved/closed.

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you already write its possibility to solve by $1-\frac yx$.Can you do more clear your ques? – iostream007 Jun 21 '13 at 13:29
@iostream007 I have changed the formatting of the title so as to make it take up less vertical space -- this is a policy to ensure that the scarce space on the main page is distributed evenly over the questions. See here for more information. Please take this into consideration for future questions. Thanks in advance. – Lord_Farin Jun 21 '13 at 13:41
@Lord_Farin I'll remember it – iostream007 Jun 21 '13 at 13:42
up vote 2 down vote accepted

$1-\frac yx$ is the best you will do for most purposes. Sometimes the original will be better, depending on the rest of the expression.

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Here's how to remember: it's always easy to add or subtract fractions with the same denominator. (If you cut a pie into eighths, and you select seven eighths of it, and take away four eigths, you're still left with three eighths.)

So $$ \frac{x - y}{z} = \frac{x}{z} - \frac{y}{z} $$

In your case $x = z$ and the first fraction simplifies to $1$ (eight eighths of a pie minus three eighths of a pie is five eighths of a pie).

If you try to do the same reasoning with denominators of a fraction, you'll get junk (four eighths of a pie minus four sevenths of a pie $\neq$ four negative oneths of a pie). So don't try to simplify something like $$ \frac{x}{x - y}. $$

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You can turn it to $\left(1-\dfrac yx\right)$ as you said .

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