Question

请计算这道分式题

x^2-16 x
———— + ——
x^2+8x 16 x-4

Answer 1

x^2-16 x
———— + ——
x^2+8x+16 x-4

(x+4)(x-4) x
=———— + ——
(x+4)² x-4

x-4 x
= ——— + ——
x+4 x-4

(x-4)²+x(x+4)
=———————
(x+4)(x-4)
(x-4)²+x(x+4)
=———————
(x+4)(x-4)
2x²-4x+16
=———————
x²-16

Answer 2

(x^2-16)/(x^2+8x+16)+x/(x-4)
=(x+4)(x-4)/(x+4)^2+x/(x-4)
=(x-4)/(x+4)+x/(x-4)
=(x-4)^2/(x+4)(x-4)+x(x+4)/(x-4)(x+4)
=[(x-4)^2+x(x+4)]/(x-4)(x+4)
=(x^2-8x+16+x^2+4x)/(x-4)(x+4)
=(2x^2-4x+16)/(x-4)(x+4)
=2(x^2-2x+8)/(x-4)(x+4)

Answer 3

x^2-16 x
———— + ——
x^2+8x +16 x-4

=(x+4)(x-4)/(x+4)(x+4) + x/(x-4)

=(x-4)/(x+4) + x/(x-4)
=[(x-4)(x-4)+x(x+4) ]/(x+4)(x-4)
=2(x-4)(x+2)/(x+4)(x-4)
=2(x^2-2x+8)/(x-4)(x+4)

Answer 4

原式=（x+4）（x-4）/(x+4)^2+x/(x-4)=(x^2-8x+16+x^2+4x)/(x^2-16)=2(x^2-2x+8)/[(x+4)(x-4)]

Answer 5

x^2-16 x
———— + ——
x^2+8x+16 x-4

(x+4)(x-4) x
=———— + ——
(x+4)² x-4

x-4 x
= ——— + ——
x+4 x-4

(x-4)²+x(x+4)
=———————
(x+4)(x-4)
(x-4)²+x(x+4)
=———————
(x+4)(x-4)
2x²-4x+16
=———————
x²-16
2(x²-2x+8)
=———————=
x²-16