Chapter 9.6, Problem 7MRE

To determine

Tofind:the solution of the given equation by simplifying the equation.

Answer to Problem 7MRE

The value of the equation is $\frac{5\left(\text{2r+t}\right)}{\left(\text{r-t}\right)\left(\text{r+t}\right)}$ .

Explanation of Solution

Given:

  $\frac{{\text{4r}}^{\text{2}}{\text{-t}}^{\text{2}}}{{\text{r}}^{\text{2}}{\text{-t}}^{\text{2}}}\text{÷}\frac{\text{2r-t}}{\text{5}}$ .

Concept used:

Division of the fraction can be done by changing division to multiplication and reciprocating the second fraction.

Algebraic identities:

  $\left({\text{a}}^{\text{2}}{\text{-b}}^{\text{2}}\right)\text{=}\left(\text{a+b}\right)\left(\text{a-b}\right)$ .

Calculation:

According to the given equation:

  $\frac{{\text{4r}}^{\text{2}}{\text{-t}}^{\text{2}}}{{\text{r}}^{\text{2}}{\text{-t}}^{\text{2}}}\text{÷}\frac{\text{2r-t}}{\text{5}}$ .

Rewrite the multiplication as:

  $\frac{{\text{4r}}^{\text{2}}{\text{-t}}^{\text{2}}}{{\text{r}}^{\text{2}}{\text{-t}}^{\text{2}}}\times \frac{5}{\text{2r-t}}$ .

Make factor out of it if possible:

  $\frac{\left(\text{2r-t}\right)\left(\text{2r+t}\right)}{\left(\text{r-t}\right)\left(\text{r+t}\right)}\text{.}\frac{\text{5}}{\text{2r-t}}$ .

Cancelling the $\text{2r-t}$:

  $\frac{\left(\text{2r+t}\right)}{\left(\text{r-t}\right)\left(\text{r+t}\right)}\text{.5}$

Hence the value of the equation is $\frac{5\left(\text{2r+t}\right)}{\left(\text{r-t}\right)\left(\text{r+t}\right)}$ .