How do you multiply and simplify #\frac { 6x + 6} { 6x + 18} \cdot \frac { 2x + 6} { 6x ^ { 2} - 6}#?

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Answer 1 · 2017-05-29T15:23:01

#frac(1)(3 x - 3)#

We have: #frac(6 x + 6)(6 x + 18) cdot frac(2 x + 6)(6 x^(2) - 6)#

First, let's factor numbers out of the expressions:

#= frac(6 (x + 1))(6 (x + 3)) cdot frac(2 (x + 3))(6 (x^(2) - 1))#

The denominator of the second fraction can be factorised, as it is a difference of squares:

#= frac(6 (x + 1))(6 (x + 3)) cdot frac(2 (x + 3))(6 (x + 1)(x - 1))#

Then, let's simplify the fractions:

#= frac(1)(1) cdot frac(2)(6 (x - 1))#

#= frac(1)(3 (x - 1))#

#= frac(1)(3 x - 3)#