Question

Algebra ll

Please, Help.

step by step answer, if you can.

Answer 1

`(2x+12)/(x-2)`

Explanation:

The perimeter of the rectangle is the sum of all 4 sides. There are two sides with length
`(x+1)/(x+2)` each and the other two sides have length
`(9x+14)/(x^2-4)` each. Now, we sum all of them.

Perimeter =
`(9x+14)/(x^2-4)+(9x+14)/(x^2-4)+(x+1)/(x+2)+(x+1)/(x+2)\\=2((9x+14)/(x^2-4))+2((x+1)/(x+2))\\=(18x+28)/(x^2-4)+(2x+2)/(x+2)\\=(18x+28)/((x-2)(x+2))+(2x+2)/(x+2)\\=(18x+28+(x-2)(2x+2))/((x-2)(x+2))\\=(18x+28+2x^2+2x-4x-4)/((x-2)(x+2))\\=(2x^2+16x+24)/((x-2)(x+2))\\=(2(x^2+8x+12))/((x-2)(x+2))\\=(2(x+2)(x+6))/((x-2)(x+2))\\=(2(x+6))/((x-2))\\=(2x+12)/(x-2)`