解方程:(x的平方+3x-8)/(x的平方+10x+25)-[1-5/(x+5)]的平方=1/(x+5)(求过程)

题目

解方程:(x的平方+3x-8)/(x的平方+10x+25)-[1-5/(x+5)]的平方=1/(x+5)(求过程)

答案

(x^2+3x-8)/(x^2+10x+25)-[1-5/(x+5)]^2=1/(x+5)
(x^2+3x-8)/(x+5)^2-[(x+5-5)/(x+5)]^2=1/(x+5)
(x^2+3x-8)/(x+5)^2-[x/(x+5)]^2=1/(x+5)
(x^2+3x-8)/(x+5)^2-x^2/(x+5)^2=1/(x+5)
(x^2+3x-8-x^2)/(x+5)^2=1/(x+5)
(3x-8)/(x+5)^2=1/(x+5)
3x-8=x+5
2x=13
x=13/2
经检验x=13/2是方程的解