How do you simplify #(x/4-1/x)/(1/(2x)+1/4)#?

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Answer 1 · 2016-11-24T20:46:53

Please see the explanation for steps leading to: #x - 2#

Multiply by 1 in the form #(8x)/(8x)#:

#(x/4 - 1/x)/(1/(2x) + 1/4)(8x)/(8x)#

#((8x^2)/4 - (8x)/x)/((8x)/(2x) + (8x)/4)#

#(2x^2 - 8)/(4 + 2x)#

There is a common factor of 2:

#(x^2 - 4)/(x + 2)#

The numerator is the difference of two squares and that factors to the sum and the difference:

#((x - 2)(x + 2))/(x + 2)#

Common factor of #x + 2#:

#x - 2#

Simplified.