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Find the area of the rectangle.

Short Answer

Expert verified

Option (J) is the correct answer.

Step by step solution

01

Step 1. Define a rational function.

A function of the form y=pq is called a rational function, where p and q are the polynomials and q0.

02

Step 2. Define the area of the rectangle.

Area of the rectangle (A)= length × width ……….. (1)

03

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

The product of two expressions aband cd, where b0and d0, is given below.

ab.cd=acbd           ...........(2)

04

Step 4. Calculate the area of the given rectangle.

Observe the figure.

The length of the rectangle =x24x+3

The width of the rectangle role="math" localid="1648028748102" =x+3x+2

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

The area of the rectangle is

A=x24x+3x24x+3

Use (2)to find the product.

role="math" localid="1648028852316" A=x24x+3x+3x+2A=(x24)(x+3)(x+3)(x+2)=x24x+2=x222x+2=(x+2)(x2)(x+2)=x2

So, the area of the given rectangle is x2.

Therefore option (J)is the correct answer.

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