Algebra Examples

$\frac{5}{x} + \frac{2}{5} = \frac{7}{x}$

Step 1

Subtract $\frac{7}{x}$ from both sides of the equation.

$\frac{5}{x} + \frac{2}{5} - \frac{7}{x} = 0$

Step 2

Simplify $\frac{5}{x} + \frac{2}{5} - \frac{7}{x}$ .

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Step 2.1

Combine the numerators over the common denominator.

$\frac{5 - 7}{x} + \frac{2}{5} = 0$

Step 2.2

Subtract $7$ from $5$ .

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

Step 2.3

Move the negative in front of the fraction.

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

Step 3

To write $- \frac{2}{x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

Step 5

Write each expression with a common denominator of $x \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{2}{x}$ by $\frac{5}{5}$ .

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

Step 5.2

Multiply $\frac{2}{5}$ by $\frac{x}{x}$ .

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

Step 5.3

Reorder the factors of $x \cdot 5$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Factor $2$ out of $- 2 \cdot 5 + 2 x$ .

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Step 7.1.1

Factor $2$ out of $- 2 \cdot 5$ .

$\frac{2 (- 1 \cdot 5) + 2 x}{5 x} = 0$

Step 7.1.2

Factor $2$ out of $2 x$ .

$\frac{2 (- 1 \cdot 5) + 2 (x)}{5 x} = 0$

Step 7.1.3

Factor $2$ out of $2 (- 1 \cdot 5) + 2 (x)$ .

$\frac{2 (- 1 \cdot 5 + x)}{5 x} = 0$

Step 7.2

Multiply $- 1$ by $5$ .

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

Step 8

Set the numerator equal to zero.

$2 (- 5 + x) = 0$

Step 9

Solve the equation for $x$ .

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Step 9.1

Divide each term in $2 (- 5 + x) = 0$ by $2$ and simplify.

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Step 9.1.1

Divide each term in $2 (- 5 + x) = 0$ by $2$ .

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

Step 9.1.2

Simplify the left side.

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Step 9.1.2.1

Cancel the common factor of $2$ .

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Step 9.1.2.1.1

Cancel the common factor.

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

Step 9.1.2.1.2

Divide $- 5 + x$ by $1$ .

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

Step 9.1.3

Simplify the right side.

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Step 9.1.3.1

Divide $0$ by $2$ .

$- 5 + x = 0$

Step 9.2

Add $5$ to both sides of the equation.

$x = 5$