作业帮已知x/5=y/3,求x+y分之x+x-y分之y减y^2/x^2-y^2的值
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已知x/5=y/3,求x+y分之x+x-y分之y减y^2/x^2-y^2的值
已知x/5=y/3,求x+y分之x+x-y分之y减y^2/x^2-y^2的值
已知x/5=y/3,求x+y分之x+x-y分之y减y^2/x^2-y^2的值
已知x/5=y/3
y/x=3/5
x+y分之x+x-y分之y减y^2/x^2-y^2的值
=（x(x-y)+y(x+y))/(x+y)(x-y)-y^2/x^2-y^2
=（x^2+y^2)/(x^2-y^2)-y^2/x^2-y^2
=(x^2+y^2-y^2)/(x^2-y^2)
=x^2/(x^2-y^2)
=1/(1-(y/x)^2)
=1/(1-(3/5)^2)
=1/(16/25)
=25/16
由x/5=y/3得x／y=5/3
x/﹙x+y﹚＋y／﹙x－y﹚－y²／﹙x²－y²﹚
=﹙x²－xy＋xy＋y²－x²﹚／﹙x²－y²﹚
=y²／﹙x²－y²﹚
=1/﹙x²／y²－1﹚
把x／y＝5/3代入上式得
原式=1/[﹙5/3﹚²－1]
=9/16
令
x/5=y/3=t
x=5t,y=3t
5t/(5t+3t)+3t/(5t-3t)-(25t^2-9t^2)/9t^2
=5/8+3/2-16/9
=17/8-16/9
=153/72-128/72
=25/72
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