help simplifying

william · #1 $Old$ November 8th, 2008, 10:47 PM

1. x^2+3/x^2 + x-1/5

2. 3a+1/3a^2+7a+2 - a+2/2a^2-a-10

3. m^2- -5m-24/m^2-9 / m^2-10m+16/m-3

red_dog · #2 $Old$ November 9th, 2008, 02:16 AM

2) $\displaystyle\frac{3a+1}{3a^2+7a+2}-\frac{a+2}{2a^2-a-10}=\frac{3a+1}{(3a+1)(a+2)}-\frac{a+2}{(a+2)(2a-5)}=$

$=\frac{1}{a+2}-\frac{1}{2a-5}=\frac{a-7}{(a+2)(2a-5)}$

3) $\displaystyle\frac{\frac{m^2-5m-24}{m^2-9)}}{\frac{m^2-10m+16}{m-3}}=\frac{m^2-5m-24}{m^2-9}\cdot\frac{m-3}{m^2-10m+16}=$

$=\frac{(m+3)(m-8)}{(m-3)(m+3)}\cdot\frac{m-3}{(m-2)(m-8)}=\frac{1}{m-2}$