Easy the answer is B: 17 and one-third
The resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.
According to the given question.
We have an equation
![\frac{x^{2}-x-6 }{x^{2} } = \frac{x-6}{2x} +\frac{2x+12}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D-x-6%20%7D%7Bx%5E%7B2%7D%20%7D%20%3D%20%5Cfrac%7Bx-6%7D%7B2x%7D%20%2B%5Cfrac%7B2x%2B12%7D%7Bx%7D)
So, to find the resulting equation of the above equation we need to simplify.
First we will take LCD
![\frac{x^{2} -x - 6 }{x^{2} } = \frac{x -6+2(2x + 12)}{2x}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D%20-x%20-%206%20%7D%7Bx%5E%7B2%7D%20%7D%20%3D%20%5Cfrac%7Bx%20-6%2B2%282x%20%2B%2012%29%7D%7B2x%7D)
![\implies \frac{x^{2}-x-6 }{x^{2} } =\frac{x-6+4x+24}{2x}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7Bx%5E%7B2%7D-x-6%20%7D%7Bx%5E%7B2%7D%20%7D%20%3D%5Cfrac%7Bx-6%2B4x%2B24%7D%7B2x%7D)
![\implies \frac{x^{2}-x-6 }{x^{2} } = \frac{5x +18}{2x}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7Bx%5E%7B2%7D-x-6%20%7D%7Bx%5E%7B2%7D%20%7D%20%3D%20%5Cfrac%7B5x%20%2B18%7D%7B2x%7D)
Multiply both the sides by x.
![\frac{x^{2}-x-6 }{x} = \frac{5x+18}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D-x-6%20%7D%7Bx%7D%20%3D%20%5Cfrac%7B5x%2B18%7D%7B2%7D)
Again multiply both the sides by x
![2x^{2} -2x-12 = 5x^{2} +18x](https://tex.z-dn.net/?f=2x%5E%7B2%7D%20-2x-12%20%3D%205x%5E%7B2%7D%20%2B18x)
![\implies 5x^{2} -2x^{2} +18x +2x +12 = 0](https://tex.z-dn.net/?f=%5Cimplies%205x%5E%7B2%7D%20-2x%5E%7B2%7D%20%2B18x%20%2B2x%20%2B12%20%3D%200)
![\implies 3x^{2} + 18x+2x + 12 = 0](https://tex.z-dn.net/?f=%5Cimplies%203x%5E%7B2%7D%20%2B%2018x%2B2x%20%2B%2012%20%3D%200)
Factorize the above equation
⇒3x(x+6)+2(x+6) = 0
⇒(3x + 2)(x+6) = 0
⇒ x = -2/3 or x = -6
Hence, the resulting equation after simplyfing the given equation is 3x^2 + 20x + 12 = 0 and whoose solutions are x = -2/3 or x = -6.
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Answer:
Step-by-step explanation:
i can not see the pic
B in has the intersection with quadrant 1 and 3