Question

已知a=-3,b=2,求a+b和a+（-b）的值

Answer 1

分式化简得：

a/(a+b)+b/(a-b)-b²/(a²-b²)

=a(a-b)/(a²-b²) + b(a+b)/(a²-b²) -b²/(a²-b²)

=[a(a-b)+b(a+b)-b²] / (a²-b²)

=(a²-ab+ab+b²-b²) / (a²-b²)

=a²/ (a²-b²)

=1/[1-(b²/a²)]

因为：a/b=3/2

所以：b/a=2/3,则：

b²/a²=4/9

原式=1/[1-(b²/a²)]

=1/(1-4/9)

=1/(5/9)

=9/5