# 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!
$\displaystyle (x+3)^\frac{-1}{3}$ $\displaystyle -(x+3)^\frac{-4}{3}$
• 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!
$\displaystyle (x+3)^\frac{-1}{3}$ $\displaystyle -(x+3)^\frac{-4}{3}$

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

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

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

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

$\displaystyle \frac{x+2}{(x+3)^{\frac{4}{3}}}$
• 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!
$\displaystyle (x+3)^\frac{-1}{3}$ $\displaystyle -(x+3)^\frac{-4}{3}$

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