Question 205391

{{{(3x^2+7x+2)/(4x^2-16)}}} Start with the given expression.



{{{((x+2)(3x+1))/(4x^2-16)}}} Factor {{{3x^2+7x+2}}} to get {{{(x+2)(3x+1)}}}.



{{{((x+2)(3x+1))/(4(x-2)(x+2))}}} Factor {{{4x^2-16}}} to get {{{4(x-2)(x+2)}}}.



{{{(highlight((x+2))(3x+1))/(4(x-2)highlight((x+2)))}}} Highlight the common terms. 



{{{(cross((x+2))(3x+1))/(4(x-2)cross((x+2)))}}} Cancel out the common terms. 



{{{(3x+1)/(4(x-2))}}} Simplify. 



{{{(3x+1)/(4x-8)}}} Distribute



So {{{(3x^2+7x+2)/(4x^2-16)}}} simplifies to {{{(3x+1)/(4x-8)}}}.



In other words, {{{(3x^2+7x+2)/(4x^2-16)=(3x+1)/(4x-8)}}}