Simplify fraction.

**elliotfsl** · February 8th 2008, 01:57 PM

a^2 - 2ab + b^2 / a - b

**wingless** · February 8th 2008, 02:08 PM

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

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

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

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

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

$\boxed{~a-b~}$

**elliotfsl** · February 8th 2008, 02:11 PM

Originally Posted by wingless

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

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

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

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

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

$\boxed{~a-b~}$

Hey, thanks. I never knew that.

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

**wingless** · February 8th 2008, 02:19 PM

Originally Posted by elliotfsl

Hey, thanks. I never knew that.

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

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

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

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

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

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

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

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

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