<span>(x/y)+(3/y)=(x+3)/y
the answer is
the numerator for the following rational expression is x+3</span>
Answer:
The dimensions of rectangle are:
Step-by-step explanation:
Let 'l' be the length and 'w' be the width of the rectangle
- The length 'l' of the rectangle is 3ft less than twice the width 'w'.
so
![l=2w-3](https://tex.z-dn.net/?f=l%3D2w-3)
Also, the area of the rectangle is 27ft^2.
![A=27\:ft^2](https://tex.z-dn.net/?f=A%3D27%5C%3Aft%5E2)
As the area of the rectangle has the formula:
![\:A\:=\:l\times w](https://tex.z-dn.net/?f=%5C%3AA%5C%3A%3D%5C%3Al%5Ctimes%20w)
so
![27=\:l\times w](https://tex.z-dn.net/?f=27%3D%5C%3Al%5Ctimes%20w)
so the equation becomes
![27=\left(2w-3\right)\times \:w](https://tex.z-dn.net/?f=27%3D%5Cleft%282w-3%5Cright%29%5Ctimes%20%5C%3Aw)
![27=2w^2-3w](https://tex.z-dn.net/?f=27%3D2w%5E2-3w)
![2w^2-3w-27=0](https://tex.z-dn.net/?f=2w%5E2-3w-27%3D0)
![\left(w+3\right)\left(2w-9\right)=0](https://tex.z-dn.net/?f=%5Cleft%28w%2B3%5Cright%29%5Cleft%282w-9%5Cright%29%3D0)
if ![ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)](https://tex.z-dn.net/?f=ab%3D0%5C%3A%5Cmathrm%7Bthen%7D%5C%3Aa%3D0%5C%3A%5Cmathrm%7Bor%7D%5C%3Ab%3D0%5C%3A%5Cleft%28%5Cmathrm%7Bor%5C%3Aboth%7D%5C%3Aa%3D0%5C%3A%5Cmathrm%7Band%7D%5C%3Ab%3D0%5Cright%29)
![w+3=0\quad \mathrm{or}\quad \:2w-9=0](https://tex.z-dn.net/?f=w%2B3%3D0%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3A2w-9%3D0)
![w=-3,\:w=\frac{9}{2}](https://tex.z-dn.net/?f=w%3D-3%2C%5C%3Aw%3D%5Cfrac%7B9%7D%7B2%7D)
as the width can not be negative, so
ft
As
![l=2w-3](https://tex.z-dn.net/?f=l%3D2w-3)
![l=2\left(4.5\right)-3](https://tex.z-dn.net/?f=l%3D2%5Cleft%284.5%5Cright%29-3)
![l=9-3](https://tex.z-dn.net/?f=l%3D9-3)
![l=6](https://tex.z-dn.net/?f=l%3D6)
So the dimensions of rectangle are:
Answer:
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