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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.
题目详情
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.
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.
▼优质解答
答案和解析
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)
=(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)
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