Question

(a-b)/(2a+2b)-(a^2+b^2)/(b^2-a^2)

注意事项：1.本题有两个除号/
2.请注意本题是两个分数线组成的
3.请写出过程
谢谢！快！！！ 好的加分

Answer 1

(a-b)/(2a+2b)+(a²+b²)/(b²-a²)
=(a-b)/2(a+b)-(a²+b²)/(a-b)(a+b)
=[(a-b)²-2(a²+b²)]/2(a+b)(a-b)
=(a²-2ab+b²-2a²-2b²)/2(a+b)(a-b)
=-(a²+2ab+b²)/2(a²-b²)
=-(a+b)²/2(a-b)(a+b)
=-(a+b)/2(a-b)

Answer 2

(a-b)/(2a+2b)-(a^2+b^2)/(b^2-a^2)
=(a-b)/2(a+b)+(a^2+b^2)/(a^2-b^2)
=（(a-b)(a+b)+2(a^2+b^2)）/2(a+b)(a-b)
=(a^2-b^2+2a^2+2b^2)/2(a+b)(a-b)
=(3a^2+b^2)/2(a^2-b^2)

Answer 3

(a-b)/(2a+2b)-(a^2+b^2)/(b^2-a^2)
=(a-b)/2(a+b)+(a^2+b^2)/(a^2-b^2)
=（(a-b)(a+b)+2(a^2+b^2))/2(a+b)(a-b)
=(a^2-b^2+2a^2+2b^2)/2(a+b)(a-b)
=(3a^2+b^2)/2(a^2-b^2)