simplify ((1/x)-(1/2))/((1/3)-(x/6))

Question

Please simply this expression showing steps

Answer 1

Multiply the numerator and denominator by 6x (the common denominator of 2, 3 and x):

(6-3x)/(2x-x^2)=3(2-x)/(x(2-x)).

The common factor 2-x cancels out (unless x=2) and we're left with 3/x.

[Let's look at the detail of multiplying each term by 6x:

6x*1/x=6; 6x*1/2=3x; 6x*1/3=2x; 6x*x/6=x^2.]

Answer 2

Given ((1/x)-(1/2))/((1/3)-(x/6))
((2-x)/2x)/((2-x)/6)
6/2x
3/x

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