搜搜做题作业网初二上分式数学题,要写过程
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初二上分式数学题,要写过程
已知x/y=2,求x^2-xy+3y^2/x^2+xy+6y^2的值
已知x/x^2+x+1=a（a≠0）,求x^2/x^4+x^2+1的值.（用含a的代数式表示）
x^2-xy+3y^2/x^2+xy+6y^2
=(x^2-xy+3y^2)/(x^2+xy+6y^2)
=(y^2)(x^2/y^2-xy/y^2+3)/[(y^2)(x^2/y^2+xy/y^2+6)]
=(4-2+3)/(4+2+6)
=(5)/(12)
=5/12
已知：x/(x^2+x+1)=a,(x^2+x+1)/x=1/a,x+1+1/x=1/a,x+1/x=1/a-1,(x+1/x)²=(1/a-1)²
x²+2+1/x²=(1/a-1)²,x²+1/x²+1=(1/a-1)²-1,(x^4+x^2+1)/x²=(1/a)(1/a-2)
∴x²/(x^4+x^2+1)=1/[1/a(1/a-2)]
x^2/x^4+x^2+1
=x^2/(x^4+x^2+1)
=1/[1/a(1/a-2)]
=(x^2-xy+3y^2)/(x^2+xy+6y^2)
=(y^2)(x^2/y^2-xy/y^2+3)/[(y^2)(x^2/y^2+xy/y^2+6)]
=(4-2+3)/(4+2+6)
=(5)/(12)
=5/12
已知：x/(x^2+x+1)=a,(x^2+x+1)/x=1/a,x+1+1/x=1/a,x+1/x=1/a-1,(x+1/x)²=(1/a-1)²
x²+2+1/x²=(1/a-1)²,x²+1/x²+1=(1/a-1)²-1,(x^4+x^2+1)/x²=(1/a)(1/a-2)
∴x²/(x^4+x^2+1)=1/[1/a(1/a-2)]
x^2/x^4+x^2+1
=x^2/(x^4+x^2+1)
=1/[1/a(1/a-2)]