Finite Math Examples

$x - 4 (\frac{72}{x} + \frac{72}{x - 4})$

Step 1

Simplify each term.

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Step 1.1

To write $\frac{72}{x}$ as a fraction with a common denominator, multiply by $\frac{x - 4}{x - 4}$ .

$x - 4 (\frac{72}{x} \cdot \frac{x - 4}{x - 4} + \frac{72}{x - 4})$

Step 1.2

To write $\frac{72}{x - 4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$x - 4 (\frac{72}{x} \cdot \frac{x - 4}{x - 4} + \frac{72}{x - 4} \cdot \frac{x}{x})$

Step 1.3

Write each expression with a common denominator of $x (x - 4)$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{72}{x}$ by $\frac{x - 4}{x - 4}$ .

$x - 4 (\frac{72 (x - 4)}{x (x - 4)} + \frac{72}{x - 4} \cdot \frac{x}{x})$

Step 1.3.2

Multiply $\frac{72}{x - 4}$ by $\frac{x}{x}$ .

$x - 4 (\frac{72 (x - 4)}{x (x - 4)} + \frac{72 x}{(x - 4) x})$

Step 1.3.3

Reorder the factors of $(x - 4) x$ .

$x - 4 (\frac{72 (x - 4)}{x (x - 4)} + \frac{72 x}{x (x - 4)})$

Step 1.4

Combine the numerators over the common denominator.

$x - 4 \frac{72 (x - 4) + 72 x}{x (x - 4)}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $72$ out of $72 (x - 4) + 72 x$ .

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Step 1.5.1.1

Factor $72$ out of $72 x$ .

$x - 4 \frac{72 (x - 4) + 72 (x)}{x (x - 4)}$

Step 1.5.1.2

Factor $72$ out of $72 (x - 4) + 72 (x)$ .

$x - 4 \frac{72 (x - 4 + x)}{x (x - 4)}$

Step 1.5.2

Add $x$ and $x$ .

$x - 4 \frac{72 (2 x - 4)}{x (x - 4)}$

Step 1.5.3

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

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Step 1.5.3.1

Factor $2$ out of $2 x$ .

$x - 4 \frac{72 (2 (x) - 4)}{x (x - 4)}$

Step 1.5.3.2

Factor $2$ out of $- 4$ .

$x - 4 \frac{72 (2 x + 2 \cdot - 2)}{x (x - 4)}$

Step 1.5.3.3

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

$x - 4 \frac{72 (2 (x - 2))}{x (x - 4)}$

$x - 4 \frac{72 \cdot 2 (x - 2)}{x (x - 4)}$

Step 1.5.4

Multiply $72$ by $2$ .

$x - 4 \frac{144 (x - 2)}{x (x - 4)}$

Step 1.6

Multiply $- 4 \frac{144 (x - 2)}{x (x - 4)}$ .

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Step 1.6.1

Combine $- 4$ and $\frac{144 (x - 2)}{x (x - 4)}$ .

$x + \frac{- 4 (144 (x - 2))}{x (x - 4)}$

Step 1.6.2

Multiply $144$ by $- 4$ .

$x + \frac{- 576 (x - 2)}{x (x - 4)}$

Step 1.7

Move the negative in front of the fraction.

$x - \frac{576 (x - 2)}{x (x - 4)}$

Step 2

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

$x \cdot \frac{x (x - 4)}{x (x - 4)} - \frac{576 (x - 2)}{x (x - 4)}$

Step 3

Simplify terms.

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Step 3.1

Combine $x$ and $\frac{x (x - 4)}{x (x - 4)}$ .

$\frac{x (x (x - 4))}{x (x - 4)} - \frac{576 (x - 2)}{x (x - 4)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{x (x (x - 4)) - 576 (x - 2)}{x (x - 4)}$

Step 4

Simplify the numerator.

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Step 4.1

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

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Step 4.1.1

Move $x$ .

$\frac{x \cdot x (x - 4) - 576 (x - 2)}{x (x - 4)}$

Step 4.1.2

Multiply $x$ by $x$ .

$\frac{x^{2} (x - 4) - 576 (x - 2)}{x (x - 4)}$

Step 4.2

Apply the distributive property.

$\frac{x^{2} x + x^{2} \cdot - 4 - 576 (x - 2)}{x (x - 4)}$

Step 4.3

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 4.3.1

Multiply $x^{2}$ by $x$ .

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Step 4.3.1.1

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

$\frac{x^{2} x^{1} + x^{2} \cdot - 4 - 576 (x - 2)}{x (x - 4)}$

Step 4.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{2 + 1} + x^{2} \cdot - 4 - 576 (x - 2)}{x (x - 4)}$

Step 4.3.2

Add $2$ and $1$ .

$\frac{x^{3} + x^{2} \cdot - 4 - 576 (x - 2)}{x (x - 4)}$

Step 4.4

Move $- 4$ to the left of $x^{2}$ .

$\frac{x^{3} - 4 \cdot x^{2} - 576 (x - 2)}{x (x - 4)}$

Step 4.5

Apply the distributive property.

$\frac{x^{3} - 4 x^{2} - 576 x - 576 \cdot - 2}{x (x - 4)}$

Step 4.6

Multiply $- 576$ by $- 2$ .

$\frac{x^{3} - 4 x^{2} - 576 x + 1152}{x (x - 4)}$