Question 1208025
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I'll denote f(x) as simply f. A similar story will apply for g as well.


f/g = (x+1)/(x^2-x)
(1/x)/g = (x+1)/(x^2-x)
1/(x*g) = (x+1)/(x(x-1))
x*1/(x*g) = x*(x+1)/(x(x-1)) ..... multiply both sides by x.
1/g = (x+1)/(x-1)
<font color=red>g(x) = (x-1)/(x+1)</font> is the final answer.


Verification using WolframAlpha
<a href="https://www.wolframalpha.com/input?i=f%28x%29%2Fg%28x%29+when+f%28x%29+%3D+1%2Fx+and+g%28x%29+%3D+%28x-1%29%2F%28x%2B1%29">https://www.wolframalpha.com/input?i=f%28x%29%2Fg%28x%29+when+f%28x%29+%3D+1%2Fx+and+g%28x%29+%3D+%28x-1%29%2F%28x%2B1%29</a>


GeoGebra is another option.
I recommend using the CAS tool in GeoGebra.
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