How do you simplify ((x/3)-6)/(10+(4/x))(x3)610+(4x)?

1 Answer
Jul 28, 2015

(x^2-18x)/(30x+12)x218x30x+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 3x3x. 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)(x3)610+(4x)=(x3)610+(4x)3x3x=x218x30x+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)(x3)610+(4x)=x318310xx+(4x)=x18310x+4x

=(x-18)/3 * x/(10x+4)=(x^2-18x)/(30x+12)=x183x10x+4=x218x30x+12