# Factor and Simplify Algebraic Expression

• Dec 29th 2009, 10:51 AM
bearhug
Factor and Simplify Algebraic Expression
I am doing some review questions for University and don't recall how to answer a question like this (my answer should only have positive exponents) .... Thanks!
$
(x+3)^\frac{-1}{3}
$
$
-(x+3)^\frac{-4}{3}
$
• Dec 29th 2009, 11:26 AM
skeeter
Quote:

Originally Posted by bearhug
I am doing some review questions for University and don't recall how to answer a question like this (my answer should only have positive exponents) .... Thanks!
$
(x+3)^\frac{-1}{3}
$
$
-(x+3)^\frac{-4}{3}
$

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

common factor for both terms is $(x+3)^{-\frac{4}{3}}$ ...

$(x+3)^{-\frac{4}{3}}[(x+3) - 1]$

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

$\frac{x+2}{(x+3)^{\frac{4}{3}}}
$
• Dec 29th 2009, 12:30 PM
Raoh
Quote:

Originally Posted by bearhug
I am doing some review questions for University and don't recall how to answer a question like this (my answer should only have positive exponents) .... Thanks!
$
(x+3)^\frac{-1}{3}
$
$
-(x+3)^\frac{-4}{3}
$

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