Question

question

multiply: \\(\frac{n^2 - 7n}{n^2 + 2n + 1} \cdot \frac{n + 1}{2n}\\)

note: enter answer in factored form

provide your answer below:

Explanation:

Factor the first numerator

Using the Greatest Common Factor Factoring knowledge point

$$ n^2 - 7n = n(n - 7) $$

Factor the first denominator

Using the Perfect Square Trinomials knowledge point

$$ n^2 + 2n + 1 = (n + 1)^2 $$

Rewrite the multiplication expression

Using the Multiplying Rational Expressions knowledge point
We substitute the factored forms back into the original expression:

$$ \frac{n(n - 7)}{(n + 1)^2} \cdot \frac{n + 1}{2n} $$

Simplify the expression

Using the Simplifying Rational Expressions knowledge point
We combine the fractions and cancel the common factors \(n\) and \((n + 1)\) from the numerator and denominator:

$$ \frac{n(n - 7)(n + 1)}{2n(n + 1)^2} = \frac{n - 7}{2(n + 1)} $$

Answer:

\(\frac{n - 7}{2(n + 1)}\)