Respuesta :
Answer:
n
Step-by-step explanation:
[tex](\frac{2n}{6n+4})(\frac{3n+2}{3n-2})[/tex]
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:
[tex](\frac{2(n)}{2(3n+2)})(\frac{3n+2}{3n-2})\\\\=(\frac{n}{3n+2})(\frac{3n+2}{3n-2})[/tex]
Now we can multiply straight across:
[tex]\frac{n(3n+2)}{(3n+2)(3n-2)}[/tex]
Since we have the same factor on the top and bottom, this factor cancels:
[tex]\frac{n}{3n-2}[/tex]
The numerator is n.
The numerator of the simplified expression is [tex]n[/tex].
Given:
The given expression is:
[tex]\left(\dfrac{2n}{6n+4}\right)\left(\dfrac{3n+2}{3n-2}\right)[/tex]
To find:
The numerator of the simplified expression.
Explanation:
We have,
[tex]\left(\dfrac{2n}{6n+4}\right)\left(\dfrac{3n+2}{3n-2}\right)[/tex]
It can be written as:
[tex]=\left(\dfrac{2n}{2(3n+2)}\right)\left(\dfrac{3n+2}{3n-2}\right)[/tex]
[tex]=\dfrac{2n(3n+2)}{2(3n+2)(3n-2)}[/tex]
[tex]=\dfrac{n}{3n-2}[/tex]
Therefore, the numerator of the simplified expression is [tex]n[/tex].
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