Pre-Algebra Examples

$\frac{4 x + 3}{x} + \frac{24}{2 x^{2} - 8 x}$

Step 1

Simplify each term.

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Step 1.1

Factor $2 x$ out of $2 x^{2} - 8 x$ .

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Step 1.1.1

Factor $2 x$ out of $2 x^{2}$ .

$\frac{4 x + 3}{x} + \frac{24}{2 x (x) - 8 x}$

Step 1.1.2

Factor $2 x$ out of $- 8 x$ .

$\frac{4 x + 3}{x} + \frac{24}{2 x (x) + 2 x (- 4)}$

Step 1.1.3

Factor $2 x$ out of $2 x (x) + 2 x (- 4)$ .

$\frac{4 x + 3}{x} + \frac{24}{2 x (x - 4)}$

Step 1.2

Cancel the common factor of $24$ and $2$ .

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Step 1.2.1

Factor $2$ out of $24$ .

$\frac{4 x + 3}{x} + \frac{2 \cdot 12}{2 x (x - 4)}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $2 x (x - 4)$ .

$\frac{4 x + 3}{x} + \frac{2 \cdot 12}{2 (x (x - 4))}$

Step 1.2.2.2

Cancel the common factor.

$\frac{4 x + 3}{x} + \frac{2 \cdot 12}{2 (x (x - 4))}$

Step 1.2.2.3

Rewrite the expression.

$\frac{4 x + 3}{x} + \frac{12}{x (x - 4)}$

Step 2

To write $\frac{4 x + 3}{x}$ as a fraction with a common denominator, multiply by $\frac{x - 4}{x - 4}$ .

$\frac{4 x + 3}{x} \cdot \frac{x - 4}{x - 4} + \frac{12}{x (x - 4)}$

Step 3

Simplify terms.

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Step 3.1

Multiply $\frac{4 x + 3}{x}$ by $\frac{x - 4}{x - 4}$ .

$\frac{(4 x + 3) (x - 4)}{x (x - 4)} + \frac{12}{x (x - 4)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{(4 x + 3) (x - 4) + 12}{x (x - 4)}$

Step 4

Simplify the numerator.

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Step 4.1

Expand $(4 x + 3) (x - 4)$ using the FOIL Method.

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Step 4.1.1

Apply the distributive property.

$\frac{4 x (x - 4) + 3 (x - 4) + 12}{x (x - 4)}$

Step 4.1.2

Apply the distributive property.

$\frac{4 x \cdot x + 4 x \cdot - 4 + 3 (x - 4) + 12}{x (x - 4)}$

Step 4.1.3

Apply the distributive property.

$\frac{4 x \cdot x + 4 x \cdot - 4 + 3 x + 3 \cdot - 4 + 12}{x (x - 4)}$

Step 4.2

Simplify and combine like terms.

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 4.2.1.1.1

Move $x$ .

$\frac{4 (x \cdot x) + 4 x \cdot - 4 + 3 x + 3 \cdot - 4 + 12}{x (x - 4)}$

Step 4.2.1.1.2

Multiply $x$ by $x$ .

$\frac{4 x^{2} + 4 x \cdot - 4 + 3 x + 3 \cdot - 4 + 12}{x (x - 4)}$

Step 4.2.1.2

Multiply $- 4$ by $4$ .

$\frac{4 x^{2} - 16 x + 3 x + 3 \cdot - 4 + 12}{x (x - 4)}$

Step 4.2.1.3

Multiply $3$ by $- 4$ .

$\frac{4 x^{2} - 16 x + 3 x - 12 + 12}{x (x - 4)}$

Step 4.2.2

Add $- 16 x$ and $3 x$ .

$\frac{4 x^{2} - 13 x - 12 + 12}{x (x - 4)}$

Step 4.3

Add $- 12$ and $12$ .

$\frac{4 x^{2} - 13 x + 0}{x (x - 4)}$

Step 4.4

Add $4 x^{2} - 13 x$ and $0$ .

$\frac{4 x^{2} - 13 x}{x (x - 4)}$

Step 4.5

Factor $x$ out of $4 x^{2} - 13 x$ .

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Step 4.5.1

Factor $x$ out of $4 x^{2}$ .

$\frac{x (4 x) - 13 x}{x (x - 4)}$

Step 4.5.2

Factor $x$ out of $- 13 x$ .

$\frac{x (4 x) + x \cdot - 13}{x (x - 4)}$

Step 4.5.3

Factor $x$ out of $x (4 x) + x \cdot - 13$ .

$\frac{x (4 x - 13)}{x (x - 4)}$

Step 5

Cancel the common factor of $x$ .

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Step 5.1

Cancel the common factor.

$\frac{x (4 x - 13)}{x (x - 4)}$

Step 5.2

Rewrite the expression.

$\frac{4 x - 13}{x - 4}$