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

15pts! (Multiple choice answer)Please answer with work-example-1
User Akayh
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2 Answers

5 votes

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)

User Colin Lamarre
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9.2k points
3 votes

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

User Julius Guevarra
by
7.9k points

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