Question $15$

$2\mathrm{.}5/10$ pts

A student was asked to evaluate the limit given below. In answering the question, the student only provided the final answer $($as indicated below$)$ along with a limit property that the student used at some point to evaluate the limit$.$ The student was asked to provide a step$-$by$-$step explanation for their work. THERE ARE $6$ STEPS I NEED THEM IN ORDER

$\underset{x}{lim}\frac{\sqrt[\phantom{2}]{x^2-9}}{5x-15}$

Student final answer: $\frac{1}{5}$

Limit property: $\underset{x+-}{lim}\frac{1}{x^7}$ where r is a positive rational number.

First evaluate this limit on your scratch paper, showing all the steps. Then use your detailed work to help the student explain their work by matching the steps and the provided explanation.

Hint: The student used an algebraic manipulation to simplify the expression before evaluating the limit$.$

Step#$1$

Step#$2$

In the numerator, c