Question

【【【急】】】化简求值：x^2-6x+9/x+1÷x^2-9/x^2+x，其中x^2=4

化简求值：x^2-6x+9/x+1÷x^2-9/x^2+x，其中x^2=4

Answer 1

x^2=4

(x^2-6x+9)/(x+1)÷(x^2-9)/(x^2+x)
=(x-3)^2/(x+1)÷(x^2-9)/(x^2+x)
=(x-3)^2/(x+1)*(x^2+x)/(x^2-9)
=(x-3)^2/(x+1)*x(x+1)/(x-3)(x+3)
=(x-3)*x/(x+3)
=(x^2-3x)/(x+3)
=(4-3x)/(x+3)

x^2=4
x=±2

当x=2时，
(4-3x)/(x+3)
=(4-3*2)/(2+3)
=-2/5

当x=2时，
(4-3x)/(x+3)
=[4-3*(-2)]/(-2+3)
=10

Answer 2

x^2-6x+9 / x+1 ÷ x^2-9 / x^2+x
=(x-3)^2/(x+1) ÷ (x+3)(x-3) / x(x+1)
=(x-3)^2/(x-1) * x(x-1) / (x+3)(x-3)
=x(x-3)/(x+3)
=(x^2-3x)/(x+3)
当x=2时，原式=（4-3*2）/(2+3)=-2/5
当x=-2时，原式=(4+3*2)/(-2+3)=10