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)
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![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)](/uploads/image/z/225755-35-5.jpg?t=%E5%B7%B2%E7%9F%A5a%2Fx%2B2%E4%B8%8Eb%2Fx-2%E7%9A%84%E5%92%8C%E7%AD%89%E4%BA%8E4x%2Fx2-4%2C%E6%B1%82a%2Bb%E7%9A%84%E5%80%BC%EF%BC%88%E8%AF%A6%E7%BB%86%E8%BF%87%E7%A8%8B%EF%BC%89%26%23160%3B)
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.