Solve the problem

Question

The length of the rectangle is 3/x-4 feet, while its width is 2/x feet. Find its perimeter. 

 

 

 

 

 

 

 

(the answer is: 10x-16/x(x-4)ft but i need help step by step on how they got this answer)

Answer 1

Hi Cathryn,

 

The formula for the perimeter of a rectangle is P = 2L + 2W. Plug the expressions that you're given in and add.

 

2*3/(x-4) + 2*2/x

= 6/(x-4) + 4/x

 

To add these, you need a common denominator. Your common denominator is x(x-4), so you need to multiply the first  term by x/x and the second term by (x-4)/(x-4)

 

= 6*x / (x-4)*x + 4*(x-4) / x*(x-4)

= 6x / x(x-4) + (4x-16) / x(x-4)

 

Now that the denominators are the same, you can add the like terms in the numerators,

 

= (6x + 4x - 16) / x(x-4)

= (10x - 16) / x(x-4)