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

题目

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

答案

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)