The length of a rectangle is 2x+4/x^2-9 and its width is 3/x-3. Express the perimeter of the rectangle as a single fraction in simplest form.

### 2 Answers | Add Yours

The length of the rectangle is (2x+4)/(x^2-9) and its width is 3/(x-3). The perimeter of the rectangle has to be expressed as a single fraction in simplest form.

The perimeter is 2*(l + w) = 2*((2x+4)/(x^2-9) + 3/(x-3))

=> 2*((2x+4) + 3*(x + 3))/(x^2-9)

=> 2*(2x + 4 + 3x + 9)/(x^2-9)

=> 2*(5x + 13)/(x^2-9)

=> (10x + 26)/(x^2-9)

**The perimeter of the rectangle is (10x + 26)/(x^2-9)**

Length of rectange = (2x+4)/(x^2-9)

Width of rectangle = 3/(x-3) = 3(x+3) / {(x-3)(x+3)}

= (3x+9)/(x^2-9)

Perimeter of rectangle = 2*(length+width)

= 2*{(2x+4)/(x^2-9) + (3x+9)/(x^2-9)}

= 2* (2x+4+3x+9) / (x^2-9)

= 2*(5x+13)/(x^2-9)

= (10x+26)/(x^2-9)

**The perimeter of rectangle is (10x+26)/(x^2-9)**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes