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

Question

Please show all steps however simple.

 

Answer 1

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