Question

已知X/XxX+X+1 =1/4 求XxX/XxXxXxX+XxX+1的值. （X为诶克斯,x为乘）要过程和理由!

Answer 1

x/(x²+x+1)=1/4

分子分母同时除以x得

1/(x+1+1/x)=1/4

所以

x+1/x=3

x²/(x^4+x²+1)

分子分母同时除以x²得

=1/(x²+1+1/x²)

=1/[(x+1/x)²-1]

=1/[9-1]

=1/8