Question

Find the solution of the following equation. 2/(x+3) - 4/(x-3) = -6/(x+3)​

Answer 1

Answer:

3/x-1 + 1/x-3 = 4/x-2

⇒ [ 3(x-3) + 1(x-1) ] / [ (x-1)(x-3) ] = 4 / x-2

⇒ [ 3x - 9 + x -1 ] / [ (x-1)(x-3) ] = 4 / x-2 ---------------> Taking LCM

⇒ [ 4x - 10 ] / [ (x-1)(x-3) ] = 4 / x-2

⇒ (4x -10) (x - 2) = 4 (x -1)(x-3) --------------> cross multiplication

⇒ 4x2 - 18x + 20 = 4x2 - 16x + 12 ---------------> cancel the terms 4x2 on both sides

⇒ -18x + 20 = -16x + 12

⇒ -18x + 16x = -20 + 12

⇒ - 2x = - 8

⇒ x = 4

Answer 2

Answer:

2/(x+3)-4/(x-3)=-6/(x+3)

or,2/(x+3)+6/(x+3)=4/(x-3)

or,2+6/(x+3)=4/(x-3)

or,8/(x+3)=4/(x-3)

or,8x-24=4x+12

or,8x-4x=12+24

or,x=36/4

=9