Question 132392
{{{((8a^2-6a-9)/(6a^2-5a-6))/((4a^2+11a+6)/(9a^2+12a+4))}}} Start with the given expression


{{{((8a^2-6a-9)/(6a^2-5a-6))*((9a^2+12a+4)/(4a^2+11a+6))}}} Multiply the first fraction by the reciprocal of the second fraction




{{{(((2a-3)(4a+3))/(6a^2-5a-6))((9a^2+12a+4)/(4a^2+11a+6))}}}   Factor {{{8a^2-6a-9}}} to get {{{(2a-3)(4a+3)}}} 


{{{(((2a-3)(4a+3))/((2a-3)(3a+2)))((9a^2+12a+4)/(4a^2+11a+6))}}}   Factor {{{6a^2-5a-6}}} to get {{{(2a-3)(3a+2)}}} 


{{{(((2a-3)(4a+3))/((2a-3)(3a+2)))(((3a+2)(3a+2))/(4a^2+11a+6))}}}   Factor {{{9a^2+12a+4}}} to get {{{(3a+2)(3a+2)}}} 


{{{(((2a-3)(4a+3))/((2a-3)(3a+2)))(((3a+2)(3a+2))/((a+2)(4a+3)))}}}   Factor {{{4a^2+11a+6}}} to get {{{(a+2)(4a+3)}}} 



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



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



{{{(3a+2)/(a+2)}}} Simplify



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Answer:


So {{{((8a^2-6a-9)/(6a^2-5a-6))/((4a^2+11a+6)/(9a^2+12a+4))}}} simplifies to {{{(3a+2)/(a+2)}}}. In other words {{{((8a^2-6a-9)/(6a^2-5a-6))/((4a^2+11a+6)/(9a^2+12a+4))=(3a+2)/(a+2)}}}