Help? i dont get it

**madmatt** · April 7th 2009, 05:26 PM

4/1 - x + 2/(1 - x)^2

I have the answer

6-4x/(x-1)(x-1)

but i dont understand how to get there
anyhelp is greatly appreciated

thank you

**Prove It** · April 7th 2009, 05:31 PM

Originally Posted by madmatt

4/1 - x + 2/(1 - x)^2

I have the answer

6-4x/(x-1)(x-1)

but i dont understand how to get there
anyhelp is greatly appreciated

thank you

$\frac{4}{1 - x} + \frac{2}{(1 - x)^2}$ .

You need these terms to have the same denominator in order to add the numerators. To do this, multiply the first term by a cleverly disguised 1, in this case, $\frac{1 - x}{1 - x}$ .

So $\frac{4}{1 - x} + \frac{2}{(1 - x)^2} = \frac{4}{1 - x}\times \frac{1 - x}{1 - x} + \frac{2}{(1 - x)^2}$

$= \frac{4(1 - x)}{(1 - x)^2} + \frac{2}{(1 - x)^2}$

$= \frac{4(1 - x) + 2}{(1 - x)^2}$

$= \frac{4 - 4x + 2}{(1 - x)^2}$

$= \frac{6 - 4x}{(1 - x)^2}$ .

Also note that $(1 - x)^2 = (1 - x)(1 - x) = -(x - 1)(1 - x) = -[-(x - 1)(x - 1)] = (x - 1)(x - 1)$ .

**madmatt** · April 7th 2009, 05:35 PM

That helps a lot,
thank you very much

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