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(x+y+z)[(x+y)^-z^]／4y^z^-﹙x^-y^-z^﹚^,其中x=2,y=3,z=4化简求值
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(x+y+z)[(x+y)^-z^]／4y^z^-﹙x^-y^-z^﹚^,其中x=2,y=3,z=4 化简求值
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答案和解析
=(x+y+z)(x+y+z)(x+y-z)/[(2yz+x^2-y^2-z^2)(2yz-x^2+y^2+z^2)] =(x+y+z)^2(x+y-z)/{[x^2-(y-z)^2][(y+z)^2-x^2]} =(x+y+z)^2(x+y-z)/{(x+y-z)(x-y+z)(x+y+z)(y+z-x)} =(x+y+z)/[(x-y+z)(y+z-x)] =9/(3*5) =3/5
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