How do you multiply and simplify #\frac { 6x ^ { 3} + 4x ^ { 2} } { x ^ { 2} + 3x } * \frac { x ^ { 2} + 4x + 3} { 2x ^ { 2} - x - 10}#?

1 Answer
smendyka
Jun 9, 2017

See a solution process below:

Explanation:

First, factor each of the numerators and denominators to rewrite this expression as:

#(2x^2(3x + 2))/(x(x + 3)) * ((x + 1)(x + 3))/((2x - 5)(x + 2))#

Next, cancel common terms in the numerator and denominator:

#(2color(blue)(cancel(color(black)(x^2)))x(3x + 2))/(color(blue)(cancel(color(black)(x)))color(red)(cancel(color(black)((x + 3))))) * ((x + 1)color(red)(cancel(color(black)((x + 3)))))/((2x - 5)(x + 2)) =>#

#(2x(3x + 2))/1 * (x + 1)/((2x - 5)(x + 2))#

Next, we can multiply the denominators as:

#(2x(3x + 2))/1 * (x + 1)/(2x^2 - x - 10) =>#

#((2x(3x + 2)) * (x + 1))/(2x^2 - x - 10)#

Now, we can multiply the numerators as:

#((6x^2 + 4x) * (x + 1))/(2x^2 - x - 10) =>#

#(6x^3 + 6x^2 + 4x^2 + 4x)/(2x^2 - x - 10) =>#

#(6x^3 + (6 + 4)x^2 + 4x)/(2x^2 - x - 10) =>#

#(6x^3 + 10x^2 + 4x)/(2x^2 - x - 10)#

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