Question

15pts! (Multiple choice answer)Please answer with work

Answer 1

To find the area of a rectangle, we multiply the Base by the Height.                        In this case the:   Base = AB   and     Height = BC  

So to get the area, we multiply AB by BC.                                               (and we know that BC = 5x+5/x+3 and BC = [3x+9/2x-4)  

So we would do:

$\frac{5x+5}{x+3}$ x $\frac{3x+9}{2x-4}$                              

Note: When multiplying fractions together, we multiply the numerator by the numerator, and the denominator by the denominator.                                        

For example $\frac{2}{8}$ x $\frac{3}{4}$ = $\frac{6}{32}$    

Answer: $\frac{5x+5}{x+3}$ x $\frac{3x+9}{2x-4}$ = $\frac{(5x+5)(3x+9)}{(x+3)(2x-4)}$

$\frac{(5x+5)(3x+9)}{(x+3)(2x-4)}$ = $\frac{5(x+1)*3(x+3)}{(x+3)*2(x-2)}$ [Note: we are able to factorise some brackets to make the sum easier. For example we can factor out the 5 in (5x+5) to get: 5(x+1)   ]

Now lets simplify by multiplying the 5 and 3 together in the numerator:

$\frac{5(x+1)*3(x+3)}{(x+3)*2(x-2)}$ = $\frac{15 (x+1)(x+3)}{(x+3)*2(x-2)}$

If you notice, there is a (x+3) in numerator and the denominator. This means that we can cancel out the (x+3), to get the most simplified expression for the area:

$\frac{15 (x+1)(x+3)}{(x+3)*2(x-2)}$ = $\frac{15(x+1)}{2(x-2)}$

Final Simplified Answer: $\frac{15(x+1)}{2(x-2)}$ which is the last option

Answer 2

Area of rectangle:

$A=|AB|\cdot|BC|$

$|AB|=\dfrac{5x+5}{x+3},\ |BC|=\dfrac{3x+9}{2x-4}$

Substitute

$A=\dfrac{5x+5}{x+3}\cdot\dfrac{3x+9}{2x-4}=\dfrac{(5x+5)(3x+9)}{(x+3)(2x-4)}\\\\=\dfrac{5(x+1)\cdot3(x+3)}{(x+3)\cdot2(x-2)}=\dfrac{15(x+1)}{2(x-2)}=\dfrac{15x+15}{2x-4}$