Chapter 11: Q17. (page 699)

Find the area of the rectangle.

Short Answer

Expert verified

Option ( $J$ ) is the correct answer.

Step by step solution

Step 1. Define a rational function.

A function of the form $y = \frac{p}{q}$ is called a rational function, where $p$ and $q$ are the polynomials and $q \neq 0$ .

Step 2. Define the area of the rectangle.

Area of the rectangle $(A) =$ length $\times$ width ……….. (1)

Step 3. Define the product of two expressions ab and cd.

The product of two expressions $\frac{a}{b}$ and $\frac{c}{d}$ , where $b \neq 0$ and $d \neq 0$ , is given below.

$\frac{a}{b} . \frac{c}{d} = \frac{a c}{b d} ........... (2)$

Step 4. Calculate the area of the given rectangle.

Observe the figure.

The length of the rectangle $= \frac{x^{2} - 4}{x + 3}$

The width of the rectangle role="math" localid="1648028748102" $= \frac{x + 3}{x + 2}$

Use $(1)$ to find the area of the rectangle.

The area of the rectangle is

$A = (\frac{x^{2} - 4}{x + 3}) (\frac{x^{2} - 4}{x + 3})$

Use $(2)$ to find the product.

role="math" localid="1648028852316" $\begin{array}{l} A = (\frac{x^{2} - 4}{x + 3}) (\frac{x + 3}{x + 2}) \\ A = \frac{(x^{2} - 4) (x + 3)}{(x + 3) (x + 2)} \\ = \frac{x^{2} - 4}{x + 2} \\ = \frac{x^{2} - 2^{2}}{x + 2} \\ = \frac{(x + 2) (x - 2)}{(x + 2)} \\ = x - 2 \end{array}$

So, the area of the given rectangle is $x - 2$ .

Therefore option $(J)$ is the correct answer.

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Find the area of the rectangle.

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define the area of the rectangle.

Step 3. Define the product of two expressions ab and cd.

Step 4. Calculate the area of the given rectangle.

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