### Instruction: Solve for $r$: $$\frac{r+3}{r-2} = \frac{r-1}{r+1}.$$Express your answer as a fraction.### Response: Ok so we have $\frac{r+3}{r-2} = \frac{r-1}{r+1}$.
Right. So let's cross multiply.
That gives us $(r+3)(r+1) = (r-2)(r-1)$.
Ok. So we can expand both sides.
That gives us $r^2+4r+3=r^2-3r+2$.
Right. So if we subtract $r^2$ from both sides we get $4r+3=-3r+2$.
And if we add $3r$ to both sides we get $7r+3=2$.
And if we subtract $3$ from both sides we get $7r=-1$.