Question 118583
{{{((4x+8)/(6x+18))((5x+15)/(x^2-4))}}} Start with the given expression


{{{((4(x+2))/(6x+18))((5x+15)/(x^2-4))}}}   Factor {{{4x+8}}} to get {{{4(x+2)}}} 


{{{((4(x+2))/(6(x+3)))((5x+15)/(x^2-4))}}}   Factor {{{6x+18}}} to get {{{6(x+3)}}} 


{{{((4(x+2))/(6(x+3)))((5(x+3))/(x^2-4))}}}   Factor {{{5x+15}}} to get {{{5(x+3)}}} 


{{{((4(x+2))/(6(x+3)))((5(x+3))/((x+2)(x-2)))}}}   Factor {{{x^2-4}}} to get {{{(x+2)(x-2)}}} 



{{{((2*2(x+2))/(6(x+3)))((5(x+3))/((x+2)(x-2)))}}}   Factor 4 to get 2*2



{{{((2*2(x+2))/(2*3(x+3)))((5(x+3))/((x+2)(x-2)))}}}   Factor 6 to get 2*3



{{{2*2(x+2)5(x+3)/(2*3(x+3)(x+2)(x-2))}}} Combine the fractions




{{{cross(2)*2cross((x+2))5cross((x+3))/(cross(2)*3cross((x+3))cross((x+2))(x-2))}}} Cancel like terms



{{{(2*5)/3(x-2)}}} Simplify



{{{10/3(x-2)}}} Multiply



So {{{((4x+8)/(6x+18))((5x+15)/(x^2-4))}}} simplifies to {{{10/3(x-2)}}}



In other words, {{{((4x+8)/(6x+18))((5x+15)/(x^2-4))=10/3(x-2)}}}