How do you multiply and simplify #\frac { n ^ { 2} - 4} { n ^ { 2} } \cdot \frac { 7n } { n ^ { 2} + 4n - 12}#?

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Answer 1 · 2017-07-02T20:12:34

#(7n+14)/(2n+12)#

First, let's factorise everything and see what we're working with:

#(n^2-4)/n^2 xx (7n)/(n^2+4n-12)#

#((n-2)(n+2))/(n xx n) xx (7 xx n)/((x-2)(x+6))#

Now let's see what cancels out, meaning, "what is the same on the top and on the bottom"

#(cancelcolor(blue)((n-2))(n+2))/(cancelcolor(red)(n) xx n) xx (7 xx cancelcolor(red)(n))/(cancelcolor(blue)((n-2))(n+6))#

Let's clean this up a bit and see what we're left with

#(n+2)/n xx 7/(n+6)#

Now multiply straight across:

#(7(n+2))/(2(n+6))#

You can leave the answer like this or simplify

#(7n+14)/(2n+12)#