Suppose that the functions $g$ and $h$ are defined for all real nu \[ \begin{array}{l} g(x)=6 x \\ h(x)=3 x-1 \end{array} \] Write the expressions for $(g+h)(x)$ and $(g-h)(x)$ and eval \[ \begin{array}{l} (g+h)(x)=\square \\ (g-h)(x)=\square \\ (g \cdot h)(3)=\square \end{array} \]

Step 1 ：\((g+h)(x) = g(x) + h(x)\)

Step 2 ：Substitute \(g(x) = 6x\) and \(h(x) = 3x - 1\) into the equation:

Step 3 ：\((g+h)(x) = 6x + (3x - 1) = 9x - 1\)

Step 4 ：\((g-h)(x) = g(x) - h(x)\)

Step 5 ：Substitute \(g(x) = 6x\) and \(h(x) = 3x - 1\) into the equation:

Step 6 ：\((g-h)(x) = 6x - (3x - 1) = 3x + 1\)

Step 7 ：\((g \cdot h)(3)\) is obtained by multiplying the functions \(g(3)\) and \(h(3)\).

Step 8 ：Substitute \(g(3) = 6*3 = 18\) and \(h(3) = 3*3 - 1 = 8\) into the equation:

Step 9 ：\((g \cdot h)(3) = g(3) \cdot h(3) = 18 \cdot 8 = 144\)

Step 10 ：So, the final results are:

Step 11 ：\(\boxed{(g+h)(x) = 9x - 1}\)

Step 12 ：\(\boxed{(g-h)(x) = 3x + 1}\)

Step 13 ：\(\boxed{(g \cdot h)(3) = 144}\)