Question

Algebra llPlease, Help.step by step answer, if you can.

Answer 1

Answer:

$\frac{2x+12}{x-2}$

Step-by-step explanation:

The perimeter of the rectangle is the sum of all 4 sides. There are two sides with length  $\frac{x+1}{x+2}$  each and the other two sides have length  $\frac{9x+14}{x^2-4}$ each. Now, we sum all of them.

Perimeter =  $\frac{9x+14}{x^2-4}+\frac{9x+14}{x^2-4}+\frac{x+1}{x+2}+\frac{x+1}{x+2}\\=2(\frac{9x+14}{x^2-4})+2(\frac{x+1}{x+2})\\=\frac{18x+28}{x^2-4}+\frac{2x+2}{x+2}\\=\frac{18x+28}{(x-2)(x+2)}+\frac{2x+2}{x+2}\\=\frac{18x+28+(x-2)(2x+2)}{(x-2)(x+2)}\\=\frac{18x+28+2x^2+2x-4x-4}{(x-2)(x+2)}\\=\frac{2x^2+16x+24}{(x-2)(x+2)}\\=\frac{2(x^2+8x+12)}{(x-2)(x+2)}\\=\frac{2(x+2)(x+6)}{(x-2)(x+2)}\\=\frac{2(x+6)}{(x-2)}\\=\frac{2x+12}{x-2}$