x=2 is only solution while x=1 is extraneous solution
Option C is correct.
Step-by-step explanation:
We need to solve the equation
and find values of x.
Solving:
Find the LCM of denominators x-1,x and x-1. The LCM is x(x-1)
Multiply the entire equation with x(x-1)
![\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}\\\frac{1}{x-1}*x(x-1)+\frac{2}{x}*x(x-1)=\frac{x}{x-1}*x(x-1)\\Cancelling\,\,out\,\,the\,\,same\,\,terms:\\x+2(x-1)=x^2\\x+2x-2=x^2\\3x-2=x^2\\x^2-3x+2=0](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx-1%7D%2B%5Cfrac%7B2%7D%7Bx%7D%3D%5Cfrac%7Bx%7D%7Bx-1%7D%5C%5C%5Cfrac%7B1%7D%7Bx-1%7D%2Ax%28x-1%29%2B%5Cfrac%7B2%7D%7Bx%7D%2Ax%28x-1%29%3D%5Cfrac%7Bx%7D%7Bx-1%7D%2Ax%28x-1%29%5C%5CCancelling%5C%2C%5C%2Cout%5C%2C%5C%2Cthe%5C%2C%5C%2Csame%5C%2C%5C%2Cterms%3A%5C%5Cx%2B2%28x-1%29%3Dx%5E2%5C%5Cx%2B2x-2%3Dx%5E2%5C%5C3x-2%3Dx%5E2%5C%5Cx%5E2-3x%2B2%3D0)
Now, factoring the term:
![x^2-2x-x+2=0\\x(x-2)-1(x-2)=0\\(x-1)(x-2)=0\\x-1=0\,\,and\,\, x-2=0\\x=1\,\,and\,\, x=2](https://tex.z-dn.net/?f=x%5E2-2x-x%2B2%3D0%5C%5Cx%28x-2%29-1%28x-2%29%3D0%5C%5C%28x-1%29%28x-2%29%3D0%5C%5Cx-1%3D0%5C%2C%5C%2Cand%5C%2C%5C%2C%20x-2%3D0%5C%5Cx%3D1%5C%2C%5C%2Cand%5C%2C%5C%2C%20x%3D2)
The values of x are x=1 and x=2
Checking for extraneous roots:
Extraneous roots: The root that is the solution of the equation but when we put it in the equation the answer turns out not to be right.
If we put x=1 in the equation,
the denominator becomes zero i.e
which is not correct as in fraction anything divided by zero is undefined. So, x=1 is an extraneous solution.
If we put x=2 in the equation,
![\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx-1%7D%2B%5Cfrac%7B2%7D%7Bx%7D%3D%5Cfrac%7Bx%7D%7Bx-1%7D)
![\frac{1}{2-1}+\frac{2}{2}=\frac{2}{2-1}\\\frac{1}{1}+1=\frac{2}{1}\\1+1=2\\2=2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2-1%7D%2B%5Cfrac%7B2%7D%7B2%7D%3D%5Cfrac%7B2%7D%7B2-1%7D%5C%5C%5Cfrac%7B1%7D%7B1%7D%2B1%3D%5Cfrac%7B2%7D%7B1%7D%5C%5C1%2B1%3D2%5C%5C2%3D2)
So, x=2 is only solution while x=1 is extraneous solution
Option C is correct.
Keywords: Solving Equations and checking extraneous solution
Learn more about Solving Equations and checking extraneous solution at:
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<h3>
Answer: 90 degrees</h3>
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Explanation:
This figure is a kite since we have two pairs of adjacent sides that are congruent, but not all sides are the same length.
One property of kites is that the diagonals are always perpendicular (this applies to rhombuses as well). This means angle 3 is 90 degrees.
Answer:
376.9 ft²
Step-by-step explanation:
There you go the right answer
Answer:
y=-5/3+6
Step-by-step explanation:
y=mx+b
m is the slope
b is the y-intercept
y=-5/3+6
Answer:
1.15% to make 4000 after 7 years