Question

①（2a/a-1-a/a+1）*a²-1/a ②（x+2/x²-2x-x-1/x²-4x+4）÷x-4/x

Answer 1

①（2a/a-1-a/a+1）*a²-1/a
=[2a(a+1)-a(a-1)]/(a-1)(a+1）* a²-1/a
=[2a²+2a-a²+a)]/(a²-1)* a²-1/a
=[a²+3a]/a
=a+3
②（x+2/x²-2x-x-1/x²-4x+4）÷x-4/x
=[（x+2)/x(x-2) -x-1/(x-2)²] *x/(x-4)
={[（x+2)(x-2) -x(x-1)]/x(x-2)²} *x/(x-4)
={[x²-4-x²+x]/x(x-2)²} *x/(x-4)
=[(x-4)/x(x-2)²] *x/(x-4)
=1/(x-2)²

Answer 2

①【2a(a+1) - a(a-1)】÷(a² -1)(a² -1)/a=a+3
②【(x+2) (x-2)/x(x-2)² - (x-1)x/x(x-2)²】×x/(x-4)
=【(x-4)/x(x-2)²】×x/(x-4)
=1/(x-2)²