SOLUTION: Solve the following equation for the variable X 7/x-4+4/x+4=-5x/x^2-16 Thank you! That is all for today =)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the following equation for the variable X 7/x-4+4/x+4=-5x/x^2-16 Thank you! That is all for today =)      Log On


   

Question 328226: Solve the following equation for the variable X
7/x-4+4/x+4=-5x/x^2-16
Thank you!
That is all for today =)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

7%2F%28x-4%29%22%22%2B%22%224%2F%28x%2B4%29%22%22=%22%22%28-5x%29%2F%28x%5E2-16%29

Factor the denominator on the right:

7%2F%28x-4%29%22%22%2B%22%224%2F%28x%2B4%29%22%22=%22%22%28-5x%29%2F%28%28x-4%29%28x%2B4%29%29

Multiply every term through by the LCD which is (x-4)(x+4), written as red%28%28x-4%29%28x%2B4%29%2F1%29


7%2F%28x-4%29red%28%22%22%2A%22%22%29red%28%28x-4%29%28x%2B4%29%2F1%29%22%22%2B%22%224%2F%28x%2B4%29red%28%22%22%2A%22%22%29red%28%28x-4%29%28x%2B4%29%2F1%29%22%22=%22%22%28-5x%29%2F%28%28x-4%29%28x%2B4%29%29red%28%22%22%2A%22%22%29red%28%28x-4%29%28x%2B4%29%2F1%29

Cancel what will cancel:

7%2F%28cross%28x-4%29%29red%28%22%22%2A%22%22%29red%28%28cross%28x-4%29%29%28x%2B4%29%2F1%29%22%22%2B%22%224%2F%28cross%28x%2B4%29%29red%28%22%22%2A%22%22%29red%28%28x-4%29%28cross%28x%2B4%29%29%2F1%29%22%22=%22%22%28-5x%29%2F%28%28cross%28x-4%29%29%28cross%28x%2B4%29%29%29red%28%22%22%2A%22%22%29red%28%28cross%28x-4%29%29%28cross%28x%2B4%29%29%2F1%29

7red%28%22%22%2A%22%22%29red%28%28x%2B4%29%29%22%22%2B%22%224red%28%22%22%2A%22%22%29red%28%28x-4%29%29%22%22=%22%22-5x

7x%2B28%22%22%2B%22%224x-16%22%22=%22%22-5x

11x%2B12%22%22=%22%22-5x

16x%22%22=%22%22-12

x%22%22=%22%22-12%2F16

x%22%22=%22%22-3%2F4

Edwin