已知a/x+2与b/x-2的和等于4x/x2-4,求a+b的值（详细过程） 

已知a/x+2与b/x-2的和等于4x/x2-4,求a+b的值（详细过程） 
已知a/x+2与b/x-2的和等于4x/x2-4,求a+b的值（详细过程）
 

已知a/x+2与b/x-2的和等于4x/x2-4,求a+b的值（详细过程） 
a/(x+2)+b/(x-2)
=[a(x-2)+b(x+2)]/(x+2)(x-2)
=[(a+b)x+(2b-2a)]/(x²-4)
=4x/(x²-4)
所以(a+b)x+(2b-2a)=4x
即(a+b)x+(2b-2a)=4x+0
所以a+b=4

a/(x+2)+b/(x-2)=a(x-2)/(x^2-4)+b(x+2)/(x^2-4)
=[(ax-2a+bx+2b]/(x^2-4)=4x/(x^2-4)
(a+b)x+2(b-a)=4x
a+b=4
b-a=0
a=b=2
a+b=4

依题目，a/(x+2)+b/(x-2)=4x/(x^2-4),
[a(x-2)+b(x+2)]/(x^2-4)=4x/(x^2-4)
[(a+b)x-2a+2b]/(x^2-4)=4x/(x^2-4),
所以：a+b=4,-2a+2b=0,
所以a=b=2,
所以a+b=4

a/x+2+b/x-2
=[a(x-2)+b(x-2)]/(x^2-4)
=[(a+b)x-2(a-b)]/(x^2-4)
a+b=4
-2(a-b)=0
a=b=2
a+b=4

a/(x+2)+b/(x-2)=4x/(x^2-4)
[a(x-2)+b(x+2)]/[(x-2)(x+2)]=4x/(x^2-4)
(ax-2a+bx+2b)/(x^2-4)=4x/(x^2-4)
(a+b)x-2(a-b)=4x
a+b=4

a/x+2+b/x-2=4x/x2-4
a/x+b/x=4x/x2-8x/x2
2(a+d)/x2=(4x-8x)/x2
a+d=-2x

我用图片回答的,不知道能不能看清楚.