Question 336186
{{{(3x)/(x-16)-1/(x-4)}}} Start with the given expression.



{{{(3x(x-4))/((x-16)(x-4))-1/(x-4)}}} Multiply the first fraction by {{{(x-4)/(x-4)}}}



{{{(3x(x-4))/((x-16)(x-4))-(1(x-16))/((x-16)(x-4))}}} Multiply the second fraction by {{{(x-16)/(x-16)}}}



{{{(3x^2-12x)/((x-16)(x-4))-(x-16)/((x-16)(x-4))}}} Distribute.



{{{((3x^2-12x)-(x-16))/((x-16)(x-4))}}} Combine the fractions (this is possible now that the denominators are equal).



{{{(3x^2-12x-x+16)/((x-16)(x-4))}}} Distribute.



{{{(3x^2-13x+16)/((x-16)(x-4))}}} Combine like terms.



{{{(3x^2-13x+16)/(x^2-20x+64)}}} FOIL



So {{{(3x)/(x-16)-1/(x-4)=(3x^2-13x+16)/(x^2-20x+64)}}}



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