Question

In the figure, side AB is given by the expression (5x + 5)/(x + 3), and side BC is (3x + 9)/(2x - 4).

The simplified expression for the area of rectangle ABCD is _______, and the restriction on x is ____.

Answer 1

Answer:

The simplified expression for the area of rectangle ABCD is $\frac{ 15(x + 1)}{2(x - 2)}$, and the restriction on x is x≠2 .

Step-by-step explanation:

Side AB = Width of rectangle = (5x + 5)/(x + 3)

Side BC = Length of rectangle =  (3x + 9)/(2x - 4)

Area of Rectangle = Length * Width

Putting values:

$Area\,\,of\,\,rectangle =\frac{ (3x + 9)}{(2x - 4)} * \frac{(5x + 5)}{(x + 3)}$

Solving,

$Area\,\,of\,\,rectangle =\frac{ 3(x + 3)}{(2x - 4)} * \frac{5x + 5}{(x + 3)} \\Area\,\,of\,\,rectangle =\frac{ 3}{2(x - 2)} * 5x + 5\\Area\,\,of\,\,rectangle =\frac{ 3(5x + 5)}{2x - 4}\\Area\,\,of\,\,rectangle =\frac{ 15x + 15}{2x - 4}\\Area\,\,of\,\,rectangle =\frac{ 15(x + 1)}{2(x - 2)}$

The restriction on x is that x ≠ 2, because if x =2 then denominator will be zero.

So, the answer is:

The simplified expression for the area of rectangle ABCD is $\frac{ 15(x + 1)}{2(x - 2)}$, and the restriction on x is x≠2 .