How do you multiply and simplify #\frac { 3n ^ { 2} + 37n + 90} { 6} \cdot \frac { 6} { 3n ^ { 2} + 19n + 30}#?

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Answer 1 · 2017-08-11T10:17:15

#=(n+9)/(n+3)#

The first step with algebraic fractions is to factorise wherever possible.

Factorise the quadratic trinomials:

#(3n^2+37n+90)/6 xx 6/(3n^2-19n+30)#

#=((3n+10)(n+9))/6 xx 6/((3n+10)(n+3))#

Now you can simplify by cancelling like factors.

#=(cancel((3n+10))(n+9))/cancel6 xx cancel6/(cancel((3n+10))(n+3))#

#=(n+9)/(n+3)#

You cannot simplify further.