Algebra Examples

$f (x) = \frac{x}{4} - 3$ , $g (x) = 4 x^{2} + 2 x - 4$ $(f + g) (x)$

Step 1

Evaluate $f + g$ .

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Step 1.1

Replace the function designators in $f + g$ with the actual functions.

$\frac{x}{4} - 3 + 4 x^{2} + 2 x - 4$

Step 1.2

Remove parentheses.

$\frac{x}{4} - 3 + 4 x^{2} + 2 x - 4$

Step 1.3

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 3 + 4 x^{2} + \frac{x}{4} + 2 x \cdot \frac{4}{4} - 4$

Step 1.4

Simplify terms.

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Step 1.4.1

Combine $2 x$ and $\frac{4}{4}$ .

$- 3 + 4 x^{2} + \frac{x}{4} + \frac{2 x \cdot 4}{4} - 4$

Step 1.4.2

Combine the numerators over the common denominator.

$- 3 + 4 x^{2} + \frac{x + 2 x \cdot 4}{4} - 4$

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

Factor $x$ out of $x + 2 x \cdot 4$ .

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Step 1.5.1.1.1

Raise $x$ to the power of $1$ .

$- 3 + 4 x^{2} + \frac{x^{1} + 2 x \cdot 4}{4} - 4$

Step 1.5.1.1.2

Factor $x$ out of $x^{1}$ .

$- 3 + 4 x^{2} + \frac{x \cdot 1 + 2 x \cdot 4}{4} - 4$

Step 1.5.1.1.3

Factor $x$ out of $2 x \cdot 4$ .

$- 3 + 4 x^{2} + \frac{x \cdot 1 + x (2 \cdot 4)}{4} - 4$

Step 1.5.1.1.4

Factor $x$ out of $x \cdot 1 + x (2 \cdot 4)$ .

$- 3 + 4 x^{2} + \frac{x (1 + 2 \cdot 4)}{4} - 4$

Step 1.5.1.2

Multiply $2$ by $4$ .

$- 3 + 4 x^{2} + \frac{x (1 + 8)}{4} - 4$

Step 1.5.1.3

Add $1$ and $8$ .

$- 3 + 4 x^{2} + \frac{x \cdot 9}{4} - 4$

Step 1.5.2

Move $9$ to the left of $x$ .

$- 3 + 4 x^{2} + \frac{9 x}{4} - 4$

Step 1.6

Subtract $4$ from $- 3$ .

$4 x^{2} + \frac{9 x}{4} - 7$

Step 2

Evaluate $f + g$ at $x$ .

$4 {(x)}^{2} + \frac{9 (x)}{4} - 7$

Step 3

Simplify $4 {(x)}^{2} + \frac{9 (x)}{4} - 7$ .

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Step 3.1

Remove parentheses.

$4 {(x)}^{2} + \frac{9 (x)}{4} - 7$

Step 3.2

Multiply $9$ by $x$ .

$4 x^{2} + \frac{9 x}{4} - 7$