Question 349727
{{{((x+5)^2)/(x^2+2x-15)+2/(4x-12)}}} Start with the given expression.



{{{((x+5)(x+5))/(x^2+2x-15)+2/(4x-12)}}} Break up the first numerator



{{{((x+5)(x+5))/((x+5)(x-3))+2/(4x-12)}}} Factor the first denominator.



{{{((x+5)*highlight((x+5)))/(highlight((x+5))(x-3))+2/(4x-12)}}} Highlight the common terms.



{{{((x+5)*cross((x+5)))/(cross((x+5))(x-3))+2/(4x-12)}}} Cancel out the common terms.



{{{(x+5)/(x-3)+2/(4x-12)}}} Simplify



{{{(x+5)/(x-3)+2/(4(x-3))}}} Factor the second denominator.



Take note that the LCD is {{{4(x-3)}}}. So we need to get every denominator equal to the LCD so we can add the fractions.



{{{(4(x+5))/(4(x-3))+2/(4(x-3))}}} Multiply the first fraction by {{{4/4}}} to get that fraction to have the denominator equal to the LCD.



{{{(4x+20)/(4x-12)+2/(4x-12)}}} Distribute.



{{{(4x+20+2)/(4x-12)}}} Add the fractions.



{{{(4x+22)/(4x-12)}}} Combine like terms.



{{{(2(2x+11))/(4x-12)}}} Factor out a '2' from the numerator.



{{{(2(2x+11))/(2(2x-6))}}} Factor out a '2' from the denominator.



{{{(highlight(2)(2x+11))/(highlight(2)(2x-6))}}} Highlight the common terms.



{{{(cross(2)(2x+11))/(cross(2)(2x-6))}}} Cancel out the common terms.



{{{(2x+11)/(2x-6)}}} Simplify.



So {{{((x+5)^2)/(x^2+2x-15)+2/(4x-12)}}} simplifies to {{{(2x+11)/(2x-6)}}}



In other words, {{{((x+5)^2)/(x^2+2x-15)+2/(4x-12)=(2x+11)/(2x-6)}}}



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