Question

question 7
2 pts
simply each expression.
\\(\frac{2}{n+7} \div \frac{n^2+2n-8}{n-2}\\)
numerator / denominator = /

Explanation:

Step1: Rewrite division as multiplication

To divide by a fraction, multiply by its reciprocal. So, $\frac{2}{n + 7} \div \frac{n^2 + 2n - 8}{n - 2}$ becomes $\frac{2}{n + 7} \times \frac{n - 2}{n^2 + 2n - 8}$.

Step2: Factor the quadratic

Factor the quadratic in the denominator: $n^2 + 2n - 8$. We need two numbers that multiply to -8 and add to 2. Those numbers are 4 and -2. So, $n^2 + 2n - 8=(n + 4)(n - 2)$.

Step3: Simplify the expression

Substitute the factored form into the expression: $\frac{2}{n + 7} \times \frac{n - 2}{(n + 4)(n - 2)}$. The $(n - 2)$ terms cancel out, leaving $\frac{2}{(n + 7)(n + 4)}$. Expand the denominator: $(n + 7)(n + 4)=n^2 + 11n + 28$. So the simplified expression is $\frac{2}{n^2 + 11n + 28}$.

Answer:

2 / (n² + 11n + 28)