### Instruction: Simplify $\frac{x+1}{3}+\frac{2-3x}{2}$.  Express your answer as a single fraction.### Response: Ok so we need to add $\frac{x+1}{3}$ and $\frac{2-3x}{2}$.
Right. To do that we need to find the least common multiple of the two denominators.
In this case that would be 6.
So we need to rewrite each fraction with a denominator of 6.
We can do that by multiplying the first fraction by $\frac{2}{2}$ and the second fraction by $\frac{3}{3}$.
That gives us $\frac{2(x+1)}{6}+\frac{3(2-3x)}{6}$.
Now we can add the two fractions.
That gives us $\frac{2x+2+6-9x}{6}$.
And if we simplify that we get $\frac{-7x+8}{6}$.