Question 155251
{{{((4x^2-9)/(6x-9))/(4x^2+12x+9)}}} Start with the given expression



{{{((4x^2-9)/(6x-9))/((4x^2+12x+9)/1)}}} Rewrite {{{4x^2+12x+9}}} as a fraction by adding a denominator of 1



{{{((4x^2-9)/(6x-9))*(1/(4x^2+12x+9))}}} Multiply the top-most fraction by the reciprocal of the bottom-most fraction



{{{(((2x+3)(2x-3))/(6x-9))*(1/(4x^2+12x+9))}}} Factor {{{4x^2-9}}} to get {{{(2x+3)(2x-3)}}}



{{{(((2x+3)(2x-3))/(3(2x-3)))*(1/(4x^2+12x+9))}}} Factor {{{6x-9}}} to get {{{3(2x-3)}}}



{{{(((2x+3)(2x-3))/(3(2x-3)))*(1/((2x+3)(2x+3)))}}} Factor {{{4x^2+12x+9}}} to get {{{(2x+3)(2x+3)}}}




{{{((2x+3)(2x-3))/(3(2x-3)(2x+3)(2x+3))}}} Combine the fractions



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



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



{{{1/(3(2x+3))}}} Simplify



So {{{((4x^2-9)/(6x-9))/(4x^2+12x+9)}}} simplifies to {{{1/(3(2x+3))}}}



In other words, {{{((4x^2-9)/(6x-9))/(4x^2+12x+9)=1/(3(2x+3))}}} where {{{x<>-3/2}}} or {{{x<>3/2}}}



So his answer is incorrect. In the future, I would suggest checking the answer. You can check the answer by graphing the original expression and comparing it to the graph of the answer.