Question

How do you simplify `((x/3)-6)/(10+(4/x))`?

Answer 1

`(x^2-18x)/(30x+12)`

Explanation:

Multiply the top (numerator) and bottom (denominator) of the overall compound fraction by the least common multiples of the bottoms of the fractions in the numerator and denominator, which is `3x`. Use the distributive property in the top and bottom and cancel appropriately to simplify.

`((x/3)-6)/(10+(4/x))=((x/3)-6)/(10+(4/x))*(3x)/(3x)=(x^2-18x)/(30x+12)`

Alternatively, you can add the fractions in the original numerator and denominator by getting common denominators and then divide the fractions by inverting and multiplying:

`((x/3)-6)/(10+(4/x))=(x/3-18/3)/((10x)/x+(4/x))=((x-18)/3)/((10x+4)/x)`

`=(x-18)/3 * x/(10x+4)=(x^2-18x)/(30x+12)`