2/x+5 - x/x-5 =1

Question

I multiplied both side by (x+5) (x-5) or by x^2 -25 and I arrive at

-x^3+x^2+25x-25 =0 And now I am stuck. Thanks for any help

Answer 1

When you multiplied, you went astray. You should have canceled common factors.
Rather than multiplying both sides by (x+5)(x-5), you should have just placed everything over the common denominator. That means you should have gotten

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

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

That is, each fraction is just multiplied by the missing factor of the LCD. Now the equation is just

2(x-5) - x(x+5) = (x-5)(x+5)
2x-10 - x^2-5x = x^2-25
2x^2+3x-15 = 0
Now just use the quadratic formula.

Answer 2

Thanks