Question 376580
{{{3/(x^2+10x-56) - 2/(x^2+16x+28)}}} Start with the given expression.



{{{3/((x-4)(x+14)) - 2/(x^2+16x+28)}}} Factor the first denominator.



{{{3/((x-4)(x+14)) - 2/((x+2)(x+14))}}} Factor the second denominator.



Notice that the LCD is {{{(x+2)(x-4)(x+14)}}}



{{{(3(x+2))/((x+2)(x-4)(x+14)) - 2/((x+2)(x+14))}}} Multiply the first fraction by {{{(x+2)/(x+2)}}} (to get the denominator equal to the LCD)


 
{{{(3(x+2))/((x+2)(x-4)(x+14)) - (2(x-4))/((x+2)(x-4)(x+14))}}} Multiply the second fraction by {{{(x-4)/(x-4)}}} (to get the denominator equal to the LCD)



{{{(3x+6)/((x+2)(x-4)(x+14)) - (2x-8)/((x+2)(x-4)(x+14))}}} Distribute.



{{{(3x+6- (2x-8))/((x+2)(x-4)(x+14))}}} Combine the numerators and place them over the LCD



{{{(3x+6-2x+8)/((x+2)(x-4)(x+14))}}} Distribute.



{{{(x+14)/((x+2)(x-4)(x+14))}}} Combine like terms.



{{{highlight((x+14))/((x+2)(x-4)highlight((x+14)))}}} Highlight the common terms.



{{{cross((x+14))/((x+2)(x-4)cross((x+14)))}}} Cancel out the common terms.



{{{1/((x+2)(x-4))}}} Simplify



{{{1/(x^2-2x-8)}}} FOIL



So {{{3/(x^2+10x-56) - 2/(x^2+16x+28)=1/(x^2-2x-8)}}}



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