Question

Simplify the expression below. (2n/6n+4)(3n+2/3n-2)What is the numerator of the simplified expression?

Answer 1

Answer:

n

Step-by-step explanation:

$(\frac{2n}{6n+4})(\frac{3n+2}{3n-2})$

We see that in the first rational expression, both the numerator and denominator are divisible by 2.  This means we can factor a 2 out of the top and bottom and then cancel it:

$(\frac{2(n)}{2(3n+2)})(\frac{3n+2}{3n-2})\\\\=(\frac{n}{3n+2})(\frac{3n+2}{3n-2})$

Now we can multiply straight across:

$\frac{n(3n+2)}{(3n+2)(3n-2)}$

Since we have the same factor on the top and bottom, this factor cancels:

$\frac{n}{3n-2}$

The numerator is n.

Answer 2

(2n/6n+4)(3n+2/3n-2)
=2n(3n+2)/(6n+4)(3n-2)
=(6n^2 + 4n)/(18n^2 - 12n + 12n -8)
=(6n^2 + 4n)/(18n^2 - 8)
=2(3n^2 + 2n)/2(9n^2 - 4)
=(3n^2 + 2n)/(9n^2 - 4)
=n(3n+ 2)/(3^2 × n^2 - 2^2)
=n(3n+ 2)/(3n-2)(3n+2)
=n/(3n-2)
Answer:The numerator of the simplified expressions is n.