Solve Equation Algebraically not by graphing. What I did was LCD and cross multiply then stuck.
2/x+2 +3/x-1= -8/5
answer in solution set should be {-4,-1/8}
I assume you meant to type:
2/(x+2) + 3/(x-1) = -8/5
Combining terms on the left is a good first step:
$\displaystyle \frac{2(x-1)+3(x+2)}{(x+2)(x-1)}=-\frac{8}{5}$
$\displaystyle \frac{5x+4}{(x+2)(x-1)}=-\frac{8}{5}$
Cross-multiplying is a good second step:
$\displaystyle 5(5x+4)=-8(x+2)(x-1)$
Now, distributing, we will find a quadratic in $\displaystyle x$:
$\displaystyle 25x+20=-8(x^2+x-2)$
$\displaystyle 25x+20=-8x^2-8x+16$
Arrange in standard form:
$\displaystyle 8x^2+33x+4=0$
Now can you factor this? We see that we need two factors of 32 whose sum is 33...