Question 140019
{{{(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)}}} 



{{{(x+2)(3x+1)/4(x+2)(x-2)}}} Combine the fractions



{{{cross((x+2))(3x+1)/4cross((x+2))(x-2)}}} Cancel like terms



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




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Answer:



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