SOLUTION: I have been trying to solve this problem on a worksheet I have for like 2 hours and for some reason these numbers just are not clicking. I have completed other similar problems but

Algebra ->  Real-numbers -> SOLUTION: I have been trying to solve this problem on a worksheet I have for like 2 hours and for some reason these numbers just are not clicking. I have completed other similar problems but      Log On


   

Question 274521: I have been trying to solve this problem on a worksheet I have for like 2 hours and for some reason these numbers just are not clicking. I have completed other similar problems but this one is just not working. I appreciate your help :)
8x/x+3 -8 =x-14/x-3
Thank You
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is:

8x%2F%28x%2B3%29+-+8+=+%28x-14%29%2F%28x-3%29

multiply both sides of this equation by (x+3) * (x-3) to get:

%288x%2A%28x-3%29%29+-+%288%2A%28x-3%29%2A%28x%2B3%29%29+=+%28%28x-14%29%2A%28x%2B3%29%29

simplify this by removing parentheses to get:

8x%5E2+-+24x+-+8x%5E2+%2B+72+=+x%5E2+%2B+3x+-+14x+-+42

combine like terms to get:

-24x+%2B+72+=+x%5E2+-+11x+-+42

add 24x and subtract 72 from both sides of this equation to get:

+0+=+x%5E2+%2B+13x+-+42

factor this equation to get:

+0+=+%28x%2B19%29+%2A+%28x-6%29

solve for x to get:

x = -19
x = 6

plug these values into the original equation to confirm they are good.

I confirmed both values and they are both good.

your answer is x = -19 or x = 6.