Finite Math Examples

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

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x + 4, 1, 1$

Step 1.2

Remove parentheses.

$x + 4, 1, 1$

Step 1.3

The LCM of one and any expression is the expression.

$x + 4$

Step 2

Multiply each term in $\frac{x^{2}}{x + 4} - 2 = x$ by $x + 4$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{x^{2}}{x + 4} - 2 = x$ by $x + 4$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Cancel the common factor of $x + 4$ .

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Step 2.2.1.1.1

Cancel the common factor.

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

Step 2.2.1.1.2

Rewrite the expression.

$x^{2} - 2 (x + 4) = x (x + 4)$

Step 2.2.1.2

Apply the distributive property.

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

Step 2.2.1.3

Multiply $- 2$ by $4$ .

$x^{2} - 2 x - 8 = x (x + 4)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$x^{2} - 2 x - 8 = x \cdot x + x \cdot 4$

Step 2.3.2

Simplify the expression.

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Step 2.3.2.1

Multiply $x$ by $x$ .

$x^{2} - 2 x - 8 = x^{2} + x \cdot 4$

Step 2.3.2.2

Move $4$ to the left of $x$ .

$x^{2} - 2 x - 8 = x^{2} + 4 x$

Step 3

Solve the equation.

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $x^{2}$ from both sides of the equation.

$x^{2} - 2 x - 8 - x^{2} = 4 x$

Step 3.1.2

Subtract $4 x$ from both sides of the equation.

$x^{2} - 2 x - 8 - x^{2} - 4 x = 0$

Step 3.1.3

Combine the opposite terms in $x^{2} - 2 x - 8 - x^{2} - 4 x$ .

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Step 3.1.3.1

Subtract $x^{2}$ from $x^{2}$ .

$- 2 x - 8 + 0 - 4 x = 0$

Step 3.1.3.2

Add $- 2 x - 8$ and $0$ .

$- 2 x - 8 - 4 x = 0$

Step 3.1.4

Subtract $4 x$ from $- 2 x$ .

$- 6 x - 8 = 0$

Step 3.2

Add $8$ to both sides of the equation.

$- 6 x = 8$

Step 3.3

Divide each term in $- 6 x = 8$ by $- 6$ and simplify.

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Step 3.3.1

Divide each term in $- 6 x = 8$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{8}{- 6}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 6$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{8}{- 6}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{- 6}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Cancel the common factor of $8$ and $- 6$ .

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Step 3.3.3.1.1

Factor $2$ out of $8$ .

$x = \frac{2 (4)}{- 6}$

Step 3.3.3.1.2

Cancel the common factors.

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Step 3.3.3.1.2.1

Factor $2$ out of $- 6$ .

$x = \frac{2 \cdot 4}{2 \cdot - 3}$

Step 3.3.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 4}{2 \cdot - 3}$

Step 3.3.3.1.2.3

Rewrite the expression.

$x = \frac{4}{- 3}$

Step 3.3.3.2

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{3}$

Decimal Form:

$x = - 1.\overline{3}$

Mixed Number Form:

$x = - 1 \frac{1}{3}$