Finite Math Examples

$f (3) + f (7) = x^{2} + 2 x$

Step 1

Simplify $f (3) + f (7)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Move $3$ to the left of $f$ .

$3 f + f (7) = x^{2} + 2 x$

Step 1.1.2

Move $7$ to the left of $f$ .

$3 f + 7 f = x^{2} + 2 x$

Step 1.2

Add $3 f$ and $7 f$ .

$10 f = x^{2} + 2 x$

Step 2

Divide each term in $10 f = x^{2} + 2 x$ by $10$ and simplify.

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Step 2.1

Divide each term in $10 f = x^{2} + 2 x$ by $10$ .

$\frac{10 f}{10} = \frac{x^{2}}{10} + \frac{2 x}{10}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $10$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{10 f}{10} = \frac{x^{2}}{10} + \frac{2 x}{10}$

Step 2.2.1.2

Divide $f$ by $1$ .

$f = \frac{x^{2}}{10} + \frac{2 x}{10}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2$ and $10$ .

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Step 2.3.1.1

Factor $2$ out of $2 x$ .

$f = \frac{x^{2}}{10} + \frac{2 (x)}{10}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $10$ .

$f = \frac{x^{2}}{10} + \frac{2 x}{2 \cdot 5}$

Step 2.3.1.2.2

Cancel the common factor.

$f = \frac{x^{2}}{10} + \frac{2 x}{2 \cdot 5}$

Step 2.3.1.2.3

Rewrite the expression.

$f = \frac{x^{2}}{10} + \frac{x}{5}$