Question

Solve: 1/x-3 - 1/x+5 = 1/6 , x is not equal to 3 , -5.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given:

An equation 1/(x-3) - 1/(x+5) = 1/6. ( x is not equal to 3 and 5).

To Find:

The value of x in the above equation.

Solution:

The given problem can be solved using the concepts of factorization.

1. The given equation is 1/(x-3) - 1/(x+5) = 1/6,

2. The above equation can be also written as,

=>$\frac{(x+5)-(x-3)}{(x-3)(x+5)} = \frac{1}{6} ,$

=> $\frac{x+5-x+3}{(x-3)(x+5)} = \frac{1}{6} ,$

=> 48= (x-3)(x+5),

=> x² +2x - 15 = 48,

=> x² + 2x -63 = 0,

=> x² +9x - 7x -63 = 0,

=> x (x+9) -7 (x+9) = 0,

=> (x - 7) (x + 9) = 0,

=> x = 7 (OR) x = -9.

Therefore, the values of x for which the equation is satisfied are 7, -9.