Question

1/(x-3)+1/(x+5)=1/3​

Answer 1

Answer:

  x = -3 or x = 7

Step-by-step explanation:

         1/(x-3)+1/(x+5) = 1/3​

multiplying by (x-3)(x+5) on both sides,

       (x + 5) + (x -3) = (x-3)(x+5)/3

=> 2x + 2 = (x^2 -3x + 5x -15)/3

=> 6x + 6 = x^2 + 2x -15

=> x^2 + 2x - 6x - 15 - 6 = 0

=> x^2 - 4x - 21 = 0

=> x^2 - 7x + 3x - 21 = 0

=> x(x - 7) + 3(x - 7) = 0

=> (x + 3)(x -7) = 0

=> x = -3 or x = 7