91Ó°ÊÓ

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

Area of the rectangle $\left(A\right)=$ length $×$ width ……….. (1)

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

$\frac{a}{b}.\frac{c}{d}=\frac{ac}{bd}\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}\mathrm{...........}\left(2\right)$

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 $\left(1\right)$to find the area of the rectangle.

The area of the rectangle is

$A=\left(\frac{{\displaystyle x^2−4}}{{\displaystyle x+3}}\right)\left(\frac{{\displaystyle x^2−4}}{{\displaystyle x+3}}\right)$

Use $\left(2\right)$to find the product.

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

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

Therefore option $\left(J\right)$is the correct answer.