Find the quotient of the functions $f(x)=2x^2+3x-2$ and $g(x)=x-1$

Step 1 ：The quotient of two functions $f(x)$ and $g(x)$ is defined as $\frac{f(x)}{g(x)}$. So, we need to divide $f(x)$ by $g(x)$.

Step 2 ：We use polynomial division to find the quotient. We divide $2x^2+3x-2$ by $x-1$.

Step 3 ：The first term in $f(x)$ is $2x^2$, and the first term in $g(x)$ is $x$. We divide $2x^2$ by $x$ and get $2x$.

Step 4 ：We multiply $2x$ by $x-1$ and subtract this from $2x^2+3x-2$, which gives us $5x-2$.

Step 5 ：The first term in $5x-2$ is $5x$, and the first term in $g(x)$ is $x$. We divide $5x$ by $x$ and get $5$.

Step 6 ：We multiply $5$ by $x-1$ and subtract this from $5x-2$, which gives us $3$.

Step 7 ：There are no more terms in $f(x)$ to bring down, so our division is complete. The quotient is $2x+5$, and the remainder is $3$.

Step 8 ：So, the quotient of the functions $f(x)$ and $g(x)$ is $\frac{f(x)}{g(x)}=2x+5+\frac{3}{x-1}$.