Question

先化简，再求值（x/（x-2）-x/x+2）÷4x/x-2，其中x=3

Answer 1

解： （x(x+2)-x(x-2))/(x-2)(x+2)*(x-2)/4x
=(x^2+2x-x^2+2x)/(x-2)(x+2)*(x-2)/4x
=4x/(x-2)(x+2）*（x-2)/4x
=1/(x+2)
x=3
原式=1/(3+2)=1/5

Answer 2

（x/（x-2）-x/x+2）÷4x/x-2
=（x/（x-2）-x/x+2）× (x－2)／4x
=x／x－2 ×(x－2)／4x －x／(x＋2) ×(x－2)／4x
=1／4－(x－2)／4(x＋2)
=1／x＋2
再将x=3代入,有
原式=1／x＋2
=1／3＋2
=1／5