Question

计算：(1)8a/ a^2-b^2 +b/ ab+b^2 (2)(x+1)/(x^2-2x+1) -(x-1)/(x^2

Answer 1

(1)8a/ a^2-b^2 +b/ ab+b^2

=8a/(a+b)(a-b)+b/b(a+b)

=8a/(a+b)(a-b)+1/(a+b)

=(8a+a-b)/(a²-b²)

=(9a-b)/(a²-b²)

(2)(x+1)/(x^2-2x+1) -(x-1)/(x^2-1)

=(x+1)/(x-1)²-(x-1)/(x+1)(x-1)

=(x+1)/(x-1)²-1/(x+1)

=[(x+1)²-(x-1)²]/(x+1)(x-1)²

=4x/(x+1)(x-1)²