Question

分式 _ 化简求值 2两题 1.已知(1/x)-(1/y)=3,求代数式(2x-14xy-2y)/(x-2xy-y)的值

Answer 1

1.因为(1/x)-(1/y)=3

所以y-x=3xy即x-y=-3xy

所以(2x-14xy-2y)/(x-2xy-y)=[2(x-y)-14xy]/[(x-y)-2xy]

=[-6xy-14xy]/[-3xy-2xy]

=4

2.因为x+(1/x)=2

所以x^2+1=2x

所以(x^2+2x+1)/(4x^2-7x+4)=[（x^2+1）+2x]/[4(x^2+1)-7x]

=(2x+2x)/(8x-7x)

=4