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How do I solve for X in this equation? Y = X / (X-1)

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1 Answer

Hi Stan;
I MADE ONE MISTAKE, AND CORRECTED IT.  I FORGOT A NEGATIVE SIGN.  PLEASE SEE THE LAST FEW LINES.
Y = X / (X-1)
This is also...
y/1=x/(x-1)
Let's flip both...
1/y=(x-1)/x
Separate the numerators of the right side...
1/y=(x/x)-(1/x)
1/y=1-(1/x)
Subtract 1 from both sides...
(1/y)-1=1-1-(1/x)
(1/y)-1=-1/x
Please remember that 1=y/y...
(1/y)-(y/y)=-1/x
Combine the numerators of the left side...
(1-y)/y=-1/x
Flip both sides...
y/(1-y)=-x
Multiply both sides by -1...
(-1)[y/(1-y)]=(-1)(-x)
y/(y-1)=x