Break down the problem into these 2 equations.
\[fx=2x+1\]
\[fx=gx\]
Solve the 1st equation: \(fx=2x+1\).
Subtract \(2x\) from both sides.
\[fx-2x=1\]
Factor out the common term \(x\).
\[x(f-2)=1\]
Divide both sides by \(f-2\).
\[x=\frac{1}{f-2}\]
\[x=\frac{1}{f-2}\]
Solve the 2nd equation: \(fx=gx\).
Move all terms to one side.
\[fx-gx=0\]
Factor out the common term \(x\).
\[x(f-g)=0\]
Divide both sides by \(f-g\).
\[x=0\]
\[x=0\]
Collect all solutions.
\[x=\frac{1}{f-2},0\]
x=1/(f-2),0
