Question

1/x-1 -1/x+5=6/7, where x is not equal to 1 & -5..

Answer 1

I am attaching the solution. In the middle we divide both equations by 6 because it was common in both. Or you can say we carry 6 from RHS to LHS where 6 got cancel on LHS with the other 6.

Answer 2

Value of x are 2 , - 6  if

$\dfrac{1}{x-1} - \dfrac{1}{x+5} =\dfrac{6}{7}$

Given:

• $\dfrac{1}{x-1} - \dfrac{1}{x+5} =\dfrac{6}{7}$
• x ≠1 , -5

To Find:

• Solve for x

Solution:

Step 1:

$\dfrac{1}{x-1} - \dfrac{1}{x+5} =\dfrac{6}{7}$

Multiply both sides by 7(x - 1)(x + 5)

7(x + 5) - 7(x - 1) = 6(x - 1)(x + 5)

Step 2:

Simplifying LHS and RHS

7(x + 5) - 7(x - 1) = 6(x - 1)(x + 5)

7x + 35 - 7x + 7  = 6(x² + 4x - 5)

42 = 6(x² + 4x - 5)

Step 3:

Dividing both sides by 6 and transposing 7

7 =  x² + 4x - 5

0 =   x² + 4x - 12

Step 4:

Factorize using middle term split

0 =   x² + 6x - 2x - 12

=> 0 = x(x + 6) - 2(x + 6)

=> 0 = (x + 6)(x - 2)

Step 5:

Equate each factor with 0

x + 6 = 0 => x = -6

x - 2 = 0 => x = 2

Hence Value of x are 2 , - 6