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

I'm trying to reduce the below equation but I'm kind of stuck. This is what I have done so far.

$((a + c)^2 - b^2) / (4a^2c^2 - (a^2 + c^2 - b^2)^2)$

--> $(a + c - b) (a + c + b) / (4a^2c^2 - a^4 - 2a^2c^2 + 2a^2b^2 - c^4 + 2b^2c^2 - b^4)$

--> $(a + c - b) (a + c + b) / (2a^2c^2 - a^4 - + 2a^2b^2 - c^4 + 2b^2c^2 - b^4)$

--> $(a + c - b) (a + c + b) / (a^2(2c^2 - a^2 + 2b^2) + b^2(2c^2 - b^2) - c^4)$


This equation seems to grow bigger and bigger and I'm not able to reduce it. Did I do something wrong?

Thank you in advance

share|cite|improve this question
Yes, you did something wrong. The given expression has lots of structure. By multiplying out you are destroying visual structure. The bottom is a difference of two squares. Exploit that! – André Nicolas Nov 19 '11 at 1:29
up vote 5 down vote accepted

Notice the denominator is the difference of two squares just like the numerator. Indeed,


Now use $(a\pm c)^2=\color{Blue}{a^2}\pm \color{Red}{2ac}+\color{Blue}{c^2}$ and then do a simple cancellation.

share|cite|improve this answer
Thank you. I solved it. – yyc2001 Nov 19 '11 at 2:00

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.