# Simplify fraction.

• Feb 8th 2008, 01:57 PM
elliotfsl
Simplify fraction.
a^2 - 2ab + b^2 / a - b
• Feb 8th 2008, 02:08 PM
wingless
Please use parentheses. I assume you wanted to say (a^2 - 2ab + b^2) / (a-b)

$\displaystyle \frac{a^2 - 2ab + b^2}{a-b}$

Do you know that $\displaystyle a^2 - 2ab + b^2 = (a-b)^2$ ?
If you didn't know, you learned now (Nod)

$\displaystyle \frac{(a-b)^2}{a-b}$

$\displaystyle \frac{(a-b)(a-b)}{(a-b)}$

$\displaystyle \boxed{~a-b~}$
• Feb 8th 2008, 02:11 PM
elliotfsl
Quote:

Originally Posted by wingless
Please use parentheses. I assume you wanted to say (a^2 - 2ab + b^2) / (a-b)

$\displaystyle \frac{a^2 - 2ab + b^2}{a-b}$

Do you know that $\displaystyle a^2 - 2ab + b^2 = (a-b)^2$ ?
If you didn't know, you learned now (Nod)

$\displaystyle \frac{(a-b)^2}{a-b}$

$\displaystyle \frac{(a-b)(a-b)}{(a-b)}$

$\displaystyle \boxed{~a-b~}$

Hey, thanks. I never knew that. :D

Now what would it be if the denominator was a + b?
• Feb 8th 2008, 02:19 PM
wingless
Quote:

Originally Posted by elliotfsl
Hey, thanks. I never knew that. :D

Now what would it be if the denominator was a + b?

$\displaystyle \frac{a^2 - 2ab + b^2}{a+b}$

Well, there's nothing much to do with this fraction.. Start with adding and subtracting $\displaystyle 4ab$,

$\displaystyle \frac{a^2 - 2ab + b^2 + 4ab - 4ab}{a + b}$

$\displaystyle \frac{a^2 + 2ab + b^2 - 4ab}{a + b}$

$\displaystyle \frac{(a+b)^2 - 4ab}{a + b}$

$\displaystyle \frac{(a+b)^2}{a + b} - \frac{4ab}{a + b}$

$\displaystyle a + b - \frac{4ab}{a + b}$