Algebra Examples

$\frac{5}{6 x} + \frac{1}{x} = - 4$

Step 1

Add $4$ to both sides of the equation.

$\frac{5}{6 x} + \frac{1}{x} + 4 = 0$

Step 2

Simplify $\frac{5}{6 x} + \frac{1}{x} + 4$ .

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Step 2.1

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5}{6 x} + \frac{1}{x} \cdot \frac{6}{6} + 4 = 0$

Step 2.2

Write each expression with a common denominator of $6 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{1}{x}$ by $\frac{6}{6}$ .

$\frac{5}{6 x} + \frac{6}{x \cdot 6} + 4 = 0$

Step 2.2.2

Reorder the factors of $x \cdot 6$ .

$\frac{5}{6 x} + \frac{6}{6 x} + 4 = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{5 + 6}{6 x} + 4 = 0$

Step 2.4

Add $5$ and $6$ .

$\frac{11}{6 x} + 4 = 0$

Step 3

To write $4$ as a fraction with a common denominator, multiply by $\frac{6 x}{6 x}$ .

$\frac{11}{6 x} + 4 \cdot \frac{6 x}{6 x} = 0$

Step 4

Combine $4$ and $\frac{6 x}{6 x}$ .

$\frac{11}{6 x} + \frac{4 (6 x)}{6 x} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{11 + 4 (6 x)}{6 x} = 0$

Step 6

Remove parentheses.

$\frac{11 + 4 \cdot (6 x)}{6 x} = 0$

Step 7

Multiply $4$ by $6$ .

$\frac{11 + 24 x}{6 x} = 0$

Step 8

Set the numerator equal to zero.

$11 + 24 x = 0$

Step 9

Solve the equation for $x$ .

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Step 9.1

Subtract $11$ from both sides of the equation.

$24 x = - 11$

Step 9.2

Divide each term in $24 x = - 11$ by $24$ and simplify.

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Step 9.2.1

Divide each term in $24 x = - 11$ by $24$ .

$\frac{24 x}{24} = \frac{- 11}{24}$

Step 9.2.2

Simplify the left side.

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Step 9.2.2.1

Cancel the common factor of $24$ .

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Step 9.2.2.1.1

Cancel the common factor.

$\frac{24 x}{24} = \frac{- 11}{24}$

Step 9.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 11}{24}$

Step 9.2.3

Simplify the right side.

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Step 9.2.3.1

Move the negative in front of the fraction.

$x = - \frac{11}{24}$