jmc

We can combine the two terms on the left side to get $\frac{1+2x}{x-1}=5$. We then multiply both sides of this equation by $x-1$ to get rid of the fractions. This gives us $1+2x=5(x-1)$. Expanding the right side gives $1+2x=5x-5$. Subtracting $5x$ from both sides gives $1-3x=-5$, and subtracting 1 from both sides of this equation yields $-3x=-6$. Dividing both sides of this equation by $-3$ gives us our answer, $x=\boxed{2}$.