SOLUTION: Hi, I need help with solving the following equation. I can get half way through it and get stuck. Here goes... 2x over x+2-2= x-8 over x-2. I'm stuck at 2x (x-2)-2(x+2), over wha

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi, I need help with solving the following equation. I can get half way through it and get stuck. Here goes... 2x over x+2-2= x-8 over x-2. I'm stuck at 2x (x-2)-2(x+2), over wha      Log On


   

Question 285198: Hi, I need help with solving the following equation. I can get half way through it and get stuck. Here goes... 2x over x+2-2= x-8 over x-2. I'm stuck at 2x (x-2)-2(x+2), over what? is it over (x-2) (x+2)?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
2x/(x+2)-2=(x-8)/(x-2)
2x-2x-4)/(x+2)=(x-8)/(x-2)
-4/(x+2)=(x-8)/(x-2)
-4(x-2)=(x-8)*(x+2)
-4x+8=x^2-16x+2x-16
0=x^2-8x+2x+4x-8-16
0=x^2-2x-24
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-24+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-24=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%28-2%29-sqrt%28+100+%29%29%2F2%5C1+=+-4

Quadratic expression 1x%5E2%2B-2x%2B-24 can be factored:
1x%5E2%2B-2x%2B-24+=+1%28x-6%29%2A%28x--4%29
Again, the answer is: 6, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-24+%29