# Solve Equation Algebraically

• December 13th 2012, 06:31 AM
Melcarthus
Solve Equation Algebraically
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}
• December 13th 2012, 07:12 AM
MarkFL
Re: Solve Equation Algebraically
I assume you meant to type:

2/(x+2) + 3/(x-1) = -8/5

Combining terms on the left is a good first step:

$\frac{2(x-1)+3(x+2)}{(x+2)(x-1)}=-\frac{8}{5}$

$\frac{5x+4}{(x+2)(x-1)}=-\frac{8}{5}$

Cross-multiplying is a good second step:

$5(5x+4)=-8(x+2)(x-1)$

Now, distributing, we will find a quadratic in $x$:

$25x+20=-8(x^2+x-2)$

$25x+20=-8x^2-8x+16$

Arrange in standard form:

$8x^2+33x+4=0$

Now can you factor this? We see that we need two factors of 32 whose sum is 33...