题目

1.(x/x+y+2y/x+y)·xy/x+2y÷(1/x+1/y).
2.(1/a+1/b)²÷(1/a²－1/b²).
3.(3x²/4y)².2y/3x+x²/2y²÷2y²/x.
4.(a+b/a－b)².2a－2b/3a+3b－a²/a²－b²÷a/b.

提问时间：2021-03-29

答案

1.(x/(x+y)+2y/(x+y))·xy/(x+2y)÷(1/x+1/y).
=(x+2y)/（x+y)*xy/(x+2y)*xy/（x+y)
=x²y²/(x+y)²
2.(1/a+1/b)²÷(1/a²－1/b²).
=(a+b)²/a²b²÷（b²-a²)/a²b²
=-(a+b)²/a²b²*a²b²/(a+b)(a-b)
=-（a+b）/(a-b)
3.(3x²/4y)².2y/3x+x²/2y²÷2y²/x.
=9x^4/16y²*2y/3x+x³/4y^4
=3x³/8y+x³/4y^4
=(3x³y³+2x³)/8y^4
4.(a+b/a－b)².（2a－2b）/（3a+3b）－a²/a²－b²÷a/b.
=（a+b)²/（a-b）²*.2（a－b）/3（a+b）-a²/（a²－b²）÷a/b
=2（a+b)/3（a-b）-ab/(a²-b²）
=2（a+b)²/3（a²-b²）-3ab/3(a²-b²）
=（2a²+ab+2b²)/3(a²-b²)