作业帮已知a/b=3/2,求a/a+b + b/a-b - b²/a²-b²的值.
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已知a/b=3/2,求a/a+b + b/a-b - b²/a²-b²的值.
已知a/b=3/2,求a/a+b + b/a-b - b²/a²-b²的值.
已知a/b=3/2,求a/a+b + b/a-b - b²/a²-b²的值.
a/b=3/2=1.5
a=1.5b
a/(a+b)+b/(a-b)-b²/(a²-b²)
=a(a-b)/(a+b)(a-b)+b(a+b)/(a+b)(a-b)-b²/(a+b)(a-b)
=(a²-ab+ab+b²-b²)/(a+b)(a-b)
=a²/(a+b)(a-b)
=2.25b²/(1.5b+b)(1.5b-b)
=2.25b²/1.25b²
=9/5
a/a+b + b/a-b - b²/a²-b²
=(a/b)/(a/b+1)+1/(a/b-1)-1/[(a/b)^2-1]
=(3/2)/(3/2+1)+1/(3/2-1)-1/[(3/2)^2-1]
=3/5+2-4/5
=9/5
a/b=3/2 b/a=2/3
所以a/(a+b)=1/[(a+b)/a]=1/(1+b/a)=3/5
b/(a-b)=1/[(a-b)/b]=1/(a/b-1)=2
b²/(a²-b²)=1/[(a²-b²)/b²]=1/[(a/b)²-1]
=4/5
a/(a+b) + b/(a-b) - b²/(a²-b²)
=3/5+2-4/5
=9/5
a/b=3/2
设a=3k,b=2k
a/a+b + b/a-b - b²/a²-b²
=3/(3+2)+2/(3-2)-4/(9-4)
=9/5
a/a+b + b/a-b - b²/a²-b²=a²-ab+ab+b²/a²-b²-b²/a²-b²=a²/a²-b²=1/(1-b²/a²)=9/5
先把后面的式子通分
得 a^2/a^2-b^2
然后a/b=3/2改成a=3b/2带入通分的式子
最后结果是9/5
因为a/b=3/2
所以a+b/a=b/a+1=5/3,所以a/a+b=3/5
同理b/a-b=2,b/a+b=2/5
b²/a²-b²=b/a-b*b/a+b=4/5
则a/a+b + b/a-b - b²/a²-b²=3/5+2-4/5=9/5
由a/b=3/2 得b/a=2/3
所以a/(a+b)=1/[(a+b)/a]=1/(1+b/a)=3/5
b/(a-b)=1/[(a-b)/b]=1/(a/b-1)=2
b^2/(a^2-b^2)=1/[(a^2-b^2)/b^2]=1/[(a/b)^2-1]
=4/5
a/(a+b) + b/(a-b) - b^2/(a^2-b^2)
=3/5+2-4/5
=9/5
即a/a+b+b/a-b-b^2/a^2-b^2
a/a+b + b/a-b - b²/a²-b²
=a(a-b)/a²-b²+b(a+b)/a²-b²-b²/a²-b²
=a²/a²-b²
就是第一个分式分子分母同乘a-b,第二个乘a+b
再把a=3b/2代入a²/a²-b²，等于9/5
设a=3x b=2x
a/a+b + b/a-b - b²/a²-b²=
3x/3x+2x+2x/3x-2x-(2x)平方/（3x）平方-（2x）平方=
9/5
很多年没做过这题了
看不明白式子到底是谁除以谁
方法就是这 你把数代进去算下就是了
因为a/b=3/2 所以a=3 b=2
然后再化简:a/a+b + b/a-b - b²/a²-b²
=a(a-b)+b(a+b)- b²/a²-b²
=a²/a²-b²
再将a,b的值代入..得:
3²/3²-2²=9/5=1.8
a/b=3/2=1.5 a=1.5b a/(a+b)+b/(a-b)-b²/(a²-b²) =a(a-b)/(a+b)(a-b)+b(a+b)/(a+b)(a-b)-b²/(a+b)(a-b) =(a²-ab+ab+b²-b²)/(a+b)(a-b) =a²/(a+b)(a-b) =2.25b²/(1.5b+b)(1.5b-b) =2.25b²/1.25b² =9/5