Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top


$$ \text{It is given that } y= \frac{3a+2}{2a-4} \text{and }x= \frac{a+3}{a+8} \\ $$

$$ \text{Express } y \text{ in terms of } x. $$

From using $x$ to solve for $a$, I discovered that $$ a = \frac{8x-3}{1-x} $$

Then I proceeded to substitute $a$ into $y$. I did this twice to ensure no mistakes are made, and my final answer for both was

$$ \frac{22x-7}{20x-10} $$

There's a problem, the correct answer is $$ \frac{7-22x}{10-20x} $$

This makes me want to cry, more so because I checked it twice and I was very careful about my working out, here it is:

$$ \frac{2+ 3(\frac{8x-3}{1-x})}{ 2(\frac{8x-3}{1-x}) -4 } $$


$$ \frac{(\frac{2(1-x) + 3(8x-3)}{1-x})}{(\frac{-4(1-x)+2(8x-3)}{1-x})} $$


$$ \frac{2(1-x) + 3(8x-3)}{1-x} * \frac{1-x}{-4(1-x)+2(8x-3)} $$


$$ \frac{22x-7}{1-x} * \frac{1-x}{20x-10} $$

The $(1-x)$'s cancel out $$\rightarrow{}$$

$$ \frac{22x-7}{20x-10} $$

Can someone please tell me as to what I did incorrectly in the process? Thank you in advance!

share|cite|improve this question
You have actually done it perfectly. Multiply both numerator and denominator by $-1$ and you're done – Marc Mar 14 '14 at 6:24
up vote 11 down vote accepted

Your answer is $$\frac{22x-7}{20x-10}$$

And the books "correct" answer is $$\frac{7-22x}{10-20x}$$

Yes? Notice what happens when you multiply both the numerator and denominator in your answer by $-1$? You're very welcome.

share|cite|improve this answer
Ah! Thank you, I was wondering whether or not I should do that but I wasn't sure, thank you again! – Samir Chahine Mar 14 '14 at 6:33
@SamirChahine you're welcome again. :D – Sabyasachi Mar 14 '14 at 6:43
+1 for nonchalance. – G. Bach Mar 14 '14 at 16:30
@G.Bach you mean +1 for sass? – Sabyasachi Mar 14 '14 at 16:33
They are easy to get mixed up, aren't they. – G. Bach Mar 14 '14 at 16:33

You got the correct answer. You just need to multiply both numerator and denominator by -1

$$\frac{22x-7}{20x-10} = \frac{-1}{-1} \times \frac{7-22x}{10-20x}$$

share|cite|improve this answer
+1 This is a better answer than the one accepted since it makes explicit that OP original answer was correct. – Taemyr Mar 14 '14 at 9:29
@Taemyr maybe. My answer was completely tongue in cheek. I just wanted to amuse myself. Apparently it amused the OP as well. – Sabyasachi Mar 14 '14 at 9:45
Is there a reason, other than just to match the "correct" answer, to do the multiply by -1/-1? Is there a rule or convention that says the "7 - 22x" form is preferred over the "22x - 7" form? – Tim Mar 14 '14 at 17:02
I don't think there is any rule but, I think there is a generally accepted (de facto?) convention of arranging terms in a polynomial order of decreasing powers. – Brad S. Mar 14 '14 at 17:10
@BradS. If you're working with polynomial rings then it's common to write the lowest degree terms first like here – DanZimm Mar 14 '14 at 18:47

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.