Evaluate Using the Given Value f(7)=3/(7+2)- square root of 7-3

$f (7) = \frac{3}{7 + 2} - \sqrt{7 - 3}$

Step 1

Simplify each term.

Add $7$ and $2$ .

$f (7) = \frac{3}{9} - \sqrt{7 - 3}$

Cancel the common factor of $3$ and $9$ .

Factor $3$ out of $3$ .

$f (7) = \frac{3 (1)}{9} - \sqrt{7 - 3}$

Cancel the common factors.

Factor $3$ out of $9$ .

$f (7) = \frac{3 \cdot 1}{3 \cdot 3} - \sqrt{7 - 3}$

Cancel the common factor.

$f (7) = \frac{3 \cdot 1}{3 \cdot 3} - \sqrt{7 - 3}$

Rewrite the expression.

$f (7) = \frac{1}{3} - \sqrt{7 - 3}$

Subtract $3$ from $7$ .

$f (7) = \frac{1}{3} - \sqrt{4}$

Rewrite $4$ as $2^{2}$ .

$f (7) = \frac{1}{3} - \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$f (7) = \frac{1}{3} - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$f (7) = \frac{1}{3} - 2$

Step 2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$f (7) = \frac{1}{3} - 2 \cdot \frac{3}{3}$

Step 3

Combine $- 2$ and $\frac{3}{3}$ .

$f (7) = \frac{1}{3} + \frac{- 2 \cdot 3}{3}$

Step 4

Combine the numerators over the common denominator.

$f (7) = \frac{1 - 2 \cdot 3}{3}$

Step 5

Simplify the numerator.

Multiply $- 2$ by $3$ .

$f (7) = \frac{1 - 6}{3}$

Subtract $6$ from $1$ .

$f (7) = \frac{- 5}{3}$

Step 6

Move the negative in front of the fraction.

$f (7) = - \frac{5}{3}$