Question

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

Answer 1

Area of rectangle:

`A=|AB|\cdot|BC|`

`|AB|=(5x+5)/(x+3),\ |BC|=(3x+9)/(2x-4)`

Substitute

`A=(5x+5)/(x+3)\cdot(3x+9)/(2x-4)=((5x+5)(3x+9))/((x+3)(2x-4))\\\\=(5(x+1)\cdot3(x+3))/((x+3)\cdot2(x-2))=(15(x+1))/(2(x-2))=(15x+15)/(2x-4)`

Answer 2

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:

`(5x+5)/(x+3)` x
`(3x+9)/(2x-4)`

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

For example
`(2)/(8)` x
`(3)/(4)` =
`(6)/(32)`

Answer:
`(5x+5)/(x+3)` x
`(3x+9)/(2x-4)` =
`((5x+5)(3x+9))/((x+3)(2x-4))`

`((5x+5)(3x+9))/((x+3)(2x-4))` =
`(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:

`(5(x+1)*3(x+3))/((x+3)*2(x-2))` =
`(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:

`(15 (x+1)(x+3))/((x+3)*2(x-2))` =
`(15(x+1))/(2(x-2))`

Final Simplified Answer:
`(15(x+1))/(2(x-2))` which is the last option