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:
[tex]\frac{5x+5}{x+3}[/tex] x [tex]\frac{3x+9}{2x-4}[/tex]
Note: When multiplying fractions together, we multiply the numerator by the numerator, and the denominator by the denominator.
For example [tex]\frac{2}{8}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{6}{32}[/tex]
Answer: [tex]\frac{5x+5}{x+3}[/tex] x [tex]\frac{3x+9}{2x-4}[/tex] = [tex]\frac{(5x+5)(3x+9)}{(x+3)(2x-4)}[/tex]
[tex]\frac{(5x+5)(3x+9)}{(x+3)(2x-4)}[/tex] = [tex]\frac{5(x+1)*3(x+3)}{(x+3)*2(x-2)}[/tex] [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:
[tex]\frac{5(x+1)*3(x+3)}{(x+3)*2(x-2)}[/tex] = [tex]\frac{15 (x+1)(x+3)}{(x+3)*2(x-2)}[/tex]
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:
[tex]\frac{15 (x+1)(x+3)}{(x+3)*2(x-2)}[/tex] = [tex]\frac{15(x+1)}{2(x-2)}[/tex]
Final Simplified Answer: [tex]\frac{15(x+1)}{2(x-2)}[/tex] which is the last option
