Question

(a) Divide $\frac{24}{5}÷6$and explain all your steps.

(b) Divide $\frac{x^2-1}{x}÷(x+1)$and explain all your steps.

(c) Evaluate your answer to part (b) when $x=5$. Did you get the same answer you got in part (a)?Why or why not?

Short answer

Part (a) $\frac{4}{5}$.

Part (b) $\frac{x-1}{x}$

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

Step-by-step solution

Part (a) Step 1. Given information.

The given expression is$\frac{24}{5}÷6$.

Part (a) Step 2.  Simplify the expression.  

$\frac{24}{5}÷6$

Apply fraction rule.

$$\begin{gathered} \frac{24}{5}\times \frac{1}{6} \\ =\frac{6\times 4}{5}\times \frac{1}{6} \\ =\frac{4}{5} \end{gathered}$$

Part (b) Step 1. Given information. 

The given expression is$\frac{x^2-1}{x}÷(x+1)$.

Part (b)  Step 2.  Simplify the expression.  

$$\begin{gathered} \frac{x^2-1}{x}÷(x+1) \\ =\frac{x^2-1}{x}\times \frac{1}{(x+1)} \\ =\frac{(x-1)(x+1)}{x}\times \frac{1}{(x+1)} \\ =\frac{x-1}{x} \end{gathered}$$

Part (c) Step 1. Given information.

Evaluate your answer to part (b) when $x=5$.

Part (c) Step 2.  Simplify the expression. 

We have, $\frac{x-1}{x}$

Plug the value $x=5$.

$$\begin{gathered} \frac{5-1}{5} \\ =\frac{4}{5} \end{gathered}$$

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