Trigonometry Examples

$\frac{2}{9 x} - \frac{7}{12} = \frac{3}{x}$

Step 1

Subtract $\frac{3}{x}$ from both sides of the equation.

$\frac{2}{9 x} - \frac{7}{12} - \frac{3}{x} = 0$

Step 2

Simplify $\frac{2}{9 x} - \frac{7}{12} - \frac{3}{x}$ .

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Step 2.1

To write $- \frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{2}{9 x} - \frac{3}{x} \cdot \frac{9}{9} - \frac{7}{12} = 0$

Step 2.2

Write each expression with a common denominator of $9 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{3}{x}$ by $\frac{9}{9}$ .

$\frac{2}{9 x} - \frac{3 \cdot 9}{x \cdot 9} - \frac{7}{12} = 0$

Step 2.2.2

Reorder the factors of $x \cdot 9$ .

$\frac{2}{9 x} - \frac{3 \cdot 9}{9 x} - \frac{7}{12} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{2 - 3 \cdot 9}{9 x} - \frac{7}{12} = 0$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $- 3$ by $9$ .

$\frac{2 - 27}{9 x} - \frac{7}{12} = 0$

Step 2.4.2

Subtract $27$ from $2$ .

$\frac{- 25}{9 x} - \frac{7}{12} = 0$

Step 2.5

Move the negative in front of the fraction.

$- \frac{25}{9 x} - \frac{7}{12} = 0$

Step 3

Set the denominator in $\frac{25}{9 x}$ equal to $0$ to find where the expression is undefined.

$9 x = 0$

Step 4

Divide each term in $9 x = 0$ by $9$ and simplify.

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Step 4.1

Divide each term in $9 x = 0$ by $9$ .

$\frac{9 x}{9} = \frac{0}{9}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $9$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{0}{9}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{9}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $9$ .

$x = 0$

Step 5