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 \(\frac{f(x)}{g(x)} = 2x + 5 + \frac{3}{x - 1}\).