### Instruction: Solve  \[\frac{3x^2+2x+1}{x-1}=3x+1\]for $x$.### Response: We can cross-multiply and get rid of the fraction.
That gives us $(3x+1)(x-1)=3x^2+2x+1$.
If we expand the left side, we get $3x^2-2x-1=3x^2+2x+1$.
Subtracting $3x^2$ from both sides gives us $-2x-1=2x+1$.
Adding $2x$ to both sides gives us $-1=4x+1$.
Subtracting 1 from both sides gives us $-2=4x$.