Algebra Examples

$10 - \frac{13}{x} = 4 + \frac{5}{x}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $4$ from both sides of the equation.

$10 - \frac{13}{x} - 4 = \frac{5}{x}$

Step 1.2

Subtract $\frac{5}{x}$ from both sides of the equation.

$10 - \frac{13}{x} - 4 - \frac{5}{x} = 0$

Step 2

Simplify $10 - \frac{13}{x} - 4 - \frac{5}{x}$ .

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Step 2.1

Combine the numerators over the common denominator.

$10 - 4 + \frac{- 13 - 5}{x} = 0$

Step 2.2

Subtract $5$ from $- 13$ .

$10 - 4 + \frac{- 18}{x} = 0$

Step 2.3

Move the negative in front of the fraction.

$10 - 4 - \frac{18}{x} = 0$

Step 2.4

Subtract $4$ from $10$ .

$6 - \frac{18}{x} = 0$

Step 3

Factor $6$ out of $6 - \frac{18}{x}$ .

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Step 3.1

Factor $6$ out of $6$ .

$6 (1) - \frac{18}{x} = 0$

Step 3.2

Factor $6$ out of $- \frac{18}{x}$ .

$6 (1) + 6 (- \frac{3}{x}) = 0$

Step 3.3

Factor $6$ out of $6 (1) + 6 (- \frac{3}{x})$ .

$6 (1 - \frac{3}{x}) = 0$

Step 4

Write $1$ as a fraction with a common denominator.

$6 (\frac{x}{x} - \frac{3}{x}) = 0$

Step 5

Combine the numerators over the common denominator.

$6 (\frac{x - 3}{x}) = 0$

Step 6

Combine $6$ and $\frac{x - 3}{x}$ .

$\frac{6 (x - 3)}{x} = 0$

Step 7

Set the numerator equal to zero.

$6 (x - 3) = 0$

Step 8

Solve the equation for $x$ .

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Step 8.1

Divide each term in $6 (x - 3) = 0$ by $6$ and simplify.

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Step 8.1.1

Divide each term in $6 (x - 3) = 0$ by $6$ .

$\frac{6 (x - 3)}{6} = \frac{0}{6}$

Step 8.1.2

Simplify the left side.

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Step 8.1.2.1

Cancel the common factor of $6$ .

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Step 8.1.2.1.1

Cancel the common factor.

$\frac{6 (x - 3)}{6} = \frac{0}{6}$

Step 8.1.2.1.2

Divide $x - 3$ by $1$ .

$x - 3 = \frac{0}{6}$

Step 8.1.3

Simplify the right side.

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Step 8.1.3.1

Divide $0$ by $6$ .

$x - 3 = 0$

Step 8.2

Add $3$ to both sides of the equation.

$x = 3$