Algebra Examples

$f (19) = \frac{3}{19 + 2} - \sqrt{19 - 3}$

Step 1

Simplify each term.

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Step 1.1

Add $19$ and $2$ .

$f (19) = \frac{3}{21} - \sqrt{19 - 3}$

Step 1.2

Cancel the common factor of $3$ and $21$ .

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Step 1.2.1

Factor $3$ out of $3$ .

$f (19) = \frac{3 (1)}{21} - \sqrt{19 - 3}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $21$ .

$f (19) = \frac{3 \cdot 1}{3 \cdot 7} - \sqrt{19 - 3}$

Step 1.2.2.2

Cancel the common factor.

$f (19) = \frac{3 \cdot 1}{3 \cdot 7} - \sqrt{19 - 3}$

Step 1.2.2.3

Rewrite the expression.

$f (19) = \frac{1}{7} - \sqrt{19 - 3}$

Step 1.3

Subtract $3$ from $19$ .

$f (19) = \frac{1}{7} - \sqrt{16}$

Step 1.4

Rewrite $16$ as $4^{2}$ .

$f (19) = \frac{1}{7} - \sqrt{4^{2}}$

Step 1.5

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

$f (19) = \frac{1}{7} - 1 \cdot 4$

Step 1.6

Multiply $- 1$ by $4$ .

$f (19) = \frac{1}{7} - 4$

Step 2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$f (19) = \frac{1}{7} - 4 \cdot \frac{7}{7}$

Step 3

Combine $- 4$ and $\frac{7}{7}$ .

$f (19) = \frac{1}{7} + \frac{- 4 \cdot 7}{7}$

Step 4

Combine the numerators over the common denominator.

$f (19) = \frac{1 - 4 \cdot 7}{7}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 4$ by $7$ .

$f (19) = \frac{1 - 28}{7}$

Step 5.2

Subtract $28$ from $1$ .

$f (19) = \frac{- 27}{7}$

Step 6

Move the negative in front of the fraction.

$f (19) = - \frac{27}{7}$