Question

4p/p+2. к дроби со знаменателем 4-p^2

Answer 1

Ответ:

$\frac{4p}{p + 2} = \frac{8p - 4p^{2}}{4- p^{2}}$

Объяснение:

$\frac{4p}{p + 2} = \frac{4p(2 - p)}{(2 + p)(2 - p)} = \frac{8p - 4p^{2}}{4 - p^{2}}$

Answer 2

To simplify the fraction with a denominator of 4 - p^2, we need to factorize the denominator first.

The denominator 4 - p^2 can be factored as the difference of squares: (2 + p)(2 - p).

Now, let's rewrite the fraction and simplify it:

4p / (p + 2) = 4p / (p + 2) * 1/(2 + p)(2 - p) * (2 - p)/(2 - p) = (4p(2 - p)) / ((p + 2)(2 + p)(2 - p)) = (4p(2 - p)) / ((p + 2)(2^2 - p^2)) = (4p(2 - p)) / ((p + 2)(4 - p^2)) = (4p(2 - p)) / ((p + 2)(4 - p^2))

So, the simplified form of the fraction 4p / (p + 2) with a denominator of 4 - p^2 is (4p(2 - p)) / ((p + 2)(4 - p^2)).