Algebra Equation?

Question

(5 / (w+4)) - 4 = 3 / (w-2)

My answer comes out to w = 1, -1. But -1 isn't correct.

Help? Thanks.

Answer 1

(5/(w+4))-4=3/(w-2)
multiply both sides by (w+4 (w-2), assuming w+4, w-2 are different from zero;
5(w-2)-4(w+4)(w-2)=3(w+4)
5w-10-4(w^2+2w-8)=3w+12
5w-10-4w^2-8w+32=3w+12
4w^2+6w-10=0
divide by 2;
2w^2+3w-5=0
2w^2+5w-2w-5=0
w(2w+5)-1(2w+5)=0
(w-1)(2w+5)=0
w=1,-5/2 ANS.
verify:1 is a root OK
-52, lhs= 5/4-5/2 -4=5/3/2 -4=10/3-4=-2/3,
rhs=3/-5/2-2 =3/-9/2 =-2/3 , lhs =rhs. so root OK

Answer 2

-5 (w-2) +4(w-2)(w+4) = -3(w+4)

4w^2 + 8w -5w+3w + 10 - 32 + 12 =0

4w^2 +6w -10 = 0
2w^2 + 3w -5 = 0

(2w + 5)(w - 1) = 0

w = 1 or - 2.5

Answer 3

common denominator is (w+4)(w-2)

so: 5(w-2) -4(w^2+2w-8) = 3(w+4)

diatribute: 5w -10 -4w^2-8w+32=3w+12
4w^2-3w+22 =3w+12
4w^2-6w-10=0
divide by 2: 2w^2-3w-5=0
use quadractic formula: there is 5/2 and 1 for the answers.