SOLUTION: 4x/x-5 + 2/x = -4/x-5 I understand that the LCD is x(x-5) but then I get stuck

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 4x/x-5 + 2/x = -4/x-5 I understand that the LCD is x(x-5) but then I get stuck      Log On


   

Question 234394: 4x/x-5 + 2/x = -4/x-5
I understand that the LCD is x(x-5) but then I get stuck
Found 2 solutions by user_dude2008, josmiceli:
Answer by user_dude2008(1862) About Me  (Show Source):
You can put this solution on YOUR website!
4x/x-5 + 2/x = -4/x-5

Multiply every term by LCD x(x-5)

4x*x + 2(x-5) = -4x

4x^2 + 2(x-5) = -4x

4x^2 + 2x-10 = -4x

4x^2 + 2x-10 +4x = 0

4x^2 +6x -10=0

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

2x+5=0 or x-1=0

x=-5/2 or x=1 <--------- Answers

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If you multiply both sides by x%2A%28x-5%29, the
equation will still be true
4x%2F%28x-5%29+%2B+2%2Fx++=+-4%2F%28x-5%29

x%2A4x+%2B+2%2A%28x-5%29+=+-4x
4x%5E2+%2B+2x+-+10+=+-4x
4x%5E2+%2B+6x+-+10=+0
2x%5E2+%2B+3x+-+5+=+0
Use the quadratic formula to solve
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+2
b+=+3
c+=+-5
x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A2%2A%28-5%29+%29%29%2F%282%2A2%29+
x+=+%28-3+%2B-+sqrt%28+9+%2B+40+%29%29%2F4+
x+=+%28-3+%2B-+sqrt%28+49+%29%29%2F4+
x+=+%28-3+%2B+7%29%2F4
x+=+1
and
x+=+%28-3+-+7%29%2F4
x+=+-5%2F2
You can check these 2 solutions by plugging back into
the original equation