Question

(x/4−1/x)/(1/2x+1/4)

Answer 1

(x/4−1/x)=(x*x-1*4)/(4*x)=(x^2-4)/4x

(1/2x+1/4)=(1*4+2x*1)/(2x*4)=(2x+4)/8x

(x/4−1/x)/(1/2x+1/4)=
[(x^2-4)/4x]/[(2x+4)/8x]=
[8x*(x^2-4)/[4x*(2x+4)]=
(8x/4x)*[(x^2-4)/(2x+4)=
2*[(x^2-4)/(2x+4)]

x^2-4=(x+2)*(x-2)

2x+4=2*(x+2)

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

(x/4−1/x)/(1/2x+1/4)= x-2