Question

Solve the rational equations. 6/(x - 3 )= [8x^2/(x^2 - 9)] - [4x/(x + 3)]

Answer 1

6/(x - 3 )   =   [8x^2/(x^2 - 9)] - [4x/(x + 3)]

6/(x - 3 )   =   [8x^2/(x^2 - 3^2)] - [4x/(x + 3)]

6/(x - 3 )   =   [8x^2/(x - 3)(x + 3)] - [4x/(x + 3)]                [Since a^2 - b^2 = (a+b)(a - b)]

Multiply the total equation with "(x - 3)"

[ 6(x - 3) ]/(x - 3)   =   (x - 3) [8x^2/(x - 3)(x + 3)] - (x - 3) [4x/(x + 3)]

6   =   [8x^2/(x + 3)] -  [4x(x - 3)/(x + 3)]

6   =   [8x^2/(x + 3)] -  [4x^2 - 12X)/(x + 3)]

Take the LCM on right side

6   =   [8x^2 - (4x^2 - 12x)]/(x + 3)

6   =   [8x^2 - 4x^2 + 12x]/(x + 3)

6   =   [4x^2 + 12x]/(x + 3)

6   =   [4x(x + 3)]/(x + 3)

6   =   4x

x   =   6/4

x   =   3/2