Solve the Function Operation g(x)=x-9 , f(x)=(x+2)(x-1) , (g/f)(2)

$g (x) = x - 9$ , $f (x) = (x + 2) (x - 1)$ , $(\frac{g}{f}) (2)$

Step 1

Replace the function designators in $\frac{g}{f}$ with the actual functions.

$\frac{x - 9}{(x + 2) (x - 1)}$

Step 2

Evaluate $\frac{g}{f}$ at $2$ .

$\frac{(2) - 9}{((2) + 2) ((2) - 1)}$

Step 3

Simplify $\frac{(2) - 9}{((2) + 2) ((2) - 1)}$ .

Simplify the expression.

Remove parentheses.

$\frac{(2) - 9}{((2) + 2) ((2) - 1)}$

Subtract $9$ from $2$ .

$\frac{- 7}{(2 + 2) (2 - 1)}$

Simplify the denominator.

Add $2$ and $2$ .

$\frac{- 7}{4 (2 - 1)}$

Subtract $1$ from $2$ .

$\frac{- 7}{4 \cdot 1}$

Simplify the expression.

Multiply $4$ by $1$ .

$\frac{- 7}{4}$

Move the negative in front of the fraction.

$- \frac{7}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{4}$

Decimal Form:

$- 1.75$

Mixed Number Form:

$- 1 \frac{3}{4}$