Algebra Examples

$\frac{2 x - 5}{x + 5} - 4 = 0$

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.

$x + 5, 1, 1$

Step 1.2

Remove parentheses.

$x + 5, 1, 1$

Step 1.3

The LCM of one and any expression is the expression.

$x + 5$

Step 2

Multiply each term in $\frac{2 x - 5}{x + 5} - 4 = 0$ by $x + 5$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2 x - 5}{x + 5} - 4 = 0$ by $x + 5$ .

$\frac{2 x - 5}{x + 5} (x + 5) - 4 (x + 5) = 0 (x + 5)$

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 $x + 5$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{2 x - 5}{x + 5} (x + 5) - 4 (x + 5) = 0 (x + 5)$

Step 2.2.1.1.2

Rewrite the expression.

$2 x - 5 - 4 (x + 5) = 0 (x + 5)$

Step 2.2.1.2

Apply the distributive property.

$2 x - 5 - 4 x - 4 \cdot 5 = 0 (x + 5)$

Step 2.2.1.3

Multiply $- 4$ by $5$ .

$2 x - 5 - 4 x - 20 = 0 (x + 5)$

Step 2.2.2

Simplify by adding terms.

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Step 2.2.2.1

Subtract $4 x$ from $2 x$ .

$- 2 x - 5 - 20 = 0 (x + 5)$

Step 2.2.2.2

Subtract $20$ from $- 5$ .

$- 2 x - 25 = 0 (x + 5)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $0$ by $x + 5$ .

$- 2 x - 25 = 0$

Step 3

Solve the equation.

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Step 3.1

Add $25$ to both sides of the equation.

$- 2 x = 25$

Step 3.2

Divide each term in $- 2 x = 25$ by $- 2$ and simplify.

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Step 3.2.1

Divide each term in $- 2 x = 25$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{25}{- 2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{25}{- 2}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{25}{- 2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$x = - \frac{25}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{25}{2}$

Decimal Form:

$x = - 12.5$

Mixed Number Form:

$x = - 12 \frac{1}{2}$