How do you multiply and simplify #\frac { 3h ^ { 2} + 5h + 2} { 2h ^ { 2} + 9h + 10} \cdot \frac { 2h ^ { 2} + 9h + 10} { 3h ^ { 2} - 4h - 4}#?

1 Answer
John D.
Jul 19, 2017

#(h+1)/(h-2)#

Explanation:

First of all, the numerator of the second fraction and the denominator of the first fraction are the same, so you can cancel them out.

#(3h^2+5h+2)/cancel(2h^2+9h+10) * cancel(2h^2+9h+10)/(3h^2-4h-4)#

#= (3h^2+5h+2)/1 * 1/(3h^2-4h-4)#

#= (3h^2+5h+2)/(3h^2 - 4h - 4)#

Now, factor both the top and the bottom:

#= (3h^2+(2h + 3h) +2)/(3h^2 + (2h - 6h) - 4)#

#= (3h^2 + 2h + 3h + 2)/(3h^2+2h - 6h - 4)#

#= ((3h^2 + 2h) + (3h + 2))/((3h^2+2h) - (6h + 4))#

#= (h(3h+2)+(3h+2))/(h(3h+2)-2(3h+2))#

#= ((h+1)(3h+2))/((h-2)(3h+2))#

Finally, cancel out the #(3h+2)# on the top and bottom:

#= ((h+1)cancel((3h+2)))/((h-2)cancel((3h+2)))#

#= (h+1)/(h-2)#

Final Answer

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