Question

(3+2x)/(2-x)+(3x-2)/(x+2)+(x²-16x)/(4-x²)

Answer 1

(3+2x)/(2-x)+(3x-2)/(x+2)+(x²-16x)/(4-x²)

=[(3+2x)(2+x)+(3x-2)(2-x)]/(4-x²)+(x²-16x)/(4-x²)

=[6+4x+3x+2x²+6x-3x²-4+2x]/(4-x²)+(x²-16x)/(4-x²)

=(2+15x-x²)/(4-x²)+(x²-16x)/(4-x²)

=(2+15x-x²+x²-16x)/(4-x²)

=(2-x)/[(2+x)(2-x)]

=1/(x+2)