Algebra Examples

$f (x) = \frac{4 x - 28}{6 x - 7}$ at $x = 7$

Step 1

Replace the variable $x$ with $7$ in the expression.

$f (7) = \frac{4 (7) - 28}{6 (7) - 7}$

Step 2

Simplify the result.

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Step 2.1

Cancel the common factor of $4 (7) - 28$ and $6 (7) - 7$ .

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Step 2.1.1

Factor $7$ out of $4 (7)$ .

$f (7) = \frac{7 \cdot 4 - 28}{6 (7) - 7}$

Step 2.1.2

Factor $7$ out of $- 28$ .

$f (7) = \frac{7 \cdot 4 + 7 (- 4)}{6 (7) - 7}$

Step 2.1.3

Factor $7$ out of $7 \cdot 4 + 7 (- 4)$ .

$f (7) = \frac{7 \cdot (4 - 4)}{6 (7) - 7}$

Step 2.1.4

Cancel the common factors.

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Step 2.1.4.1

Factor $7$ out of $6 (7)$ .

$f (7) = \frac{7 \cdot (4 - 4)}{7 \cdot 6 - 7}$

Step 2.1.4.2

Factor $7$ out of $- 7$ .

$f (7) = \frac{7 \cdot (4 - 4)}{7 \cdot 6 + 7 (- 1)}$

Step 2.1.4.3

Factor $7$ out of $7 \cdot 6 + 7 (- 1)$ .

$f (7) = \frac{7 \cdot (4 - 4)}{7 \cdot (6 - 1)}$

Step 2.1.4.4

Cancel the common factor.

$f (7) = \frac{7 \cdot (4 - 4)}{7 \cdot (6 - 1)}$

Step 2.1.4.5

Rewrite the expression.

$f (7) = \frac{4 - 4}{6 - 1}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $4$ from $4$ .

$f (7) = \frac{0}{6 - 1}$

Step 2.2.2

Subtract $1$ from $6$ .

$f (7) = \frac{0}{5}$

Step 2.2.3

Divide $0$ by $5$ .

$f (7) = 0$

Step 2.3

The final answer is $0$ .

$0$

Step 3