Question

Prove that, for all positive values of n,
-
(2n + 3)² – (2n + 1)²/
6n +6
is equal to a/b when written in its simplest form.
What are the values of a and b?

Answer 1

Answer:

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que les paso?

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siente tengo el estilo

Answer 2

$\frac{(2n+3)^{2}-(2n+1)^{2}}{6n+6} \\ \\ =\frac{(4n^{2}+12n+9)-(4n^{2}+4n+1)}{6n+6} \\ \\ =\frac{4n^{2}+12n+9-4n^{2}-4n-1}{6n+6} \\ \\ =\frac{8n+8}{6n+6} \\ \\ =\frac{4(2n+2)}{3(2n+2)} \\ \\ =\frac{4}{3} \\ \\ \therefore \boxed{a=4, b=3}$