Question

计算:1/(x+1) * [(x-3)/(x^2 + 6x + 9) + 2/(3+x)] - x/(x^2 - 9)

Answer 1

1/(x+1) * [(x-3)/(x^2 + 6x + 9) + 2/(3+x)] - x/(x^2 - 9)

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

=(x-3+2x+6)/[(x+1)(x+3)^2]-x/(x+3)(x-3)

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

=3/(x+3)^2-x/(x+3)(x-3)

=3(x-3)/(x+3)^2(x-3)-x(x+3)/(x+3)^2(x-3)

=(3x-9-x^2-3x)/(x+3)^2(x-3)

=(3x-9-x^2-3x)/(x+3)^2(x-3)

=-(x^2+9)/(x+3)^2(x-3)