Question

(a) Multiply $\frac{7}{4}\times \frac{9}{10}$and explain all your steps.

(b) Multiply $\frac{n}{n-3}\times \frac{9}{n+3}$and explain all your steps.

(c) Evaluate your answer to part (b) when$n=7$.

Did you get the same answer you got in part (a)? Why or why not?

Short answer

Part (a) $\frac{63}{40}$

Part (b) $\frac{9n}{n^2-9}$

Part (c) Yes, both the answer are same of$\left(a\right)$and$\left(c\right)$.

Step-by-step solution

Part (a) Step 1. Given information 

The given expression is$\frac{7}{4}\times \frac{9}{10}$.

Part (a) Step 2.  Simplify the expression. 

$$\begin{gathered} \frac{7}{4}\times \frac{9}{10} \\ =\frac{63}{40} \end{gathered}$$

Part (b) Step 1. Given information. 

The given expression is$\frac{n}{n-3}\times \frac{9}{n+3}$.

Part (b)  Step 2.  Simplify the expression.  

$$\begin{gathered} \frac{n}{n-3}\times \frac{9}{n+3} \\ =\frac{9n}{n^2-3^2} \\ =\frac{9n}{n^2-9} \end{gathered}$$

Part (c) Step 1. Given information 

Evaluate your answer to part (b) when $n=7$.

Part (c) Step 2.  Simplify the expression. 

We have, $\frac{9n}{n^2-9}$

Plug the value of $n$as $7$.

$$\begin{gathered} \frac{9\left(7\right)}{7^2-9} \\ =\frac{63}{49-9} \\ =\frac{63}{40} \end{gathered}$$

Yes, we got the same answer that we got in part (a).