The roots of 1/(x-3)-1/(x+5)=1/6 are:a.x= -4, -7b.x= -7, 9c.x=4, 7d.x=-9, 7

To find the roots of the equation 1/(x-3) - 1/(x+5) = 1/6, we need to solve for x. Here are the steps:

Step 1: Simplify the equation by finding a common denominator for the fractions on the left side of the equation. The common denominator is (x-3)(x+5).

So, the equation becomes:

(x+5)/(x-3)(x+5) - (x-3)/(x-3)(x+5) = 1/6

Step 2: Simplify the equation further:

(2x+2)/(x^2+2x-15) = 1/6

Step 3: Cross multiply to get rid of the fractions:

6(2x+2) = x^2+2x-15

Step 4: Simplify the equation:

12x+12 = x^2+2x-15

Step 5: Rearrange the equation to set it equal to zero:

x^2 - 10x - 27 = 0

Step 6: Factor the equation:

(x-9)(x+3) = 0

Step 7: Set each factor equal to zero and solve for x:

x-9 = 0 => x = 9 x+3 = 0 => x = -3

So, the roots of the equation are x = 9 and x = -3. However, these options are not listed in the choices. There might be a mistake in the problem or the answer choices.