Algebra Examples

$\frac{1}{3 x^{2}} = \frac{x + 3}{2 x^{2}} - \frac{1}{6 x^{2}}$

Step 1

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

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Step 1.1

Subtract $\frac{x + 3}{2 x^{2}}$ from both sides of the equation.

$\frac{1}{3 x^{2}} - \frac{x + 3}{2 x^{2}} = - \frac{1}{6 x^{2}}$

Step 1.2

Add $\frac{1}{6 x^{2}}$ to both sides of the equation.

$\frac{1}{3 x^{2}} - \frac{x + 3}{2 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2

Simplify $\frac{1}{3 x^{2}} - \frac{x + 3}{2 x^{2}} + \frac{1}{6 x^{2}}$ .

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Step 2.1

Find the common denominator.

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Step 2.1.1

Multiply $\frac{1}{3 x^{2}}$ by $\frac{2}{2}$ .

$\frac{1}{3 x^{2}} \cdot \frac{2}{2} - \frac{x + 3}{2 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.1.2

Multiply $\frac{1}{3 x^{2}}$ by $\frac{2}{2}$ .

$\frac{2}{3 x^{2} \cdot 2} - \frac{x + 3}{2 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.1.3

Multiply $\frac{x + 3}{2 x^{2}}$ by $\frac{3}{3}$ .

$\frac{2}{3 x^{2} \cdot 2} - (\frac{x + 3}{2 x^{2}} \cdot \frac{3}{3}) + \frac{1}{6 x^{2}} = 0$

Step 2.1.4

Multiply $\frac{x + 3}{2 x^{2}}$ by $\frac{3}{3}$ .

$\frac{2}{3 x^{2} \cdot 2} - \frac{(x + 3) \cdot 3}{2 x^{2} \cdot 3} + \frac{1}{6 x^{2}} = 0$

Step 2.1.5

Reorder the factors of $3 x^{2} \cdot 2$ .

$\frac{2}{2 \cdot 3 x^{2}} - \frac{(x + 3) \cdot 3}{2 x^{2} \cdot 3} + \frac{1}{6 x^{2}} = 0$

Step 2.1.6

Multiply $2$ by $3$ .

$\frac{2}{6 x^{2}} - \frac{(x + 3) \cdot 3}{2 x^{2} \cdot 3} + \frac{1}{6 x^{2}} = 0$

Step 2.1.7

Reorder the factors of $2 x^{2} \cdot 3$ .

$\frac{2}{6 x^{2}} - \frac{(x + 3) \cdot 3}{2 \cdot 3 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.1.8

Multiply $2$ by $3$ .

$\frac{2}{6 x^{2}} - \frac{(x + 3) \cdot 3}{6 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.2

Combine the numerators over the common denominator.

$\frac{2 - (x + 3) \cdot 3}{6 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.3

Simplify each term.

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Step 2.3.1

Apply the distributive property.

$\frac{2 + (- x - 1 \cdot 3) \cdot 3}{6 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.3.2

Multiply $- 1$ by $3$ .

$\frac{2 + (- x - 3) \cdot 3}{6 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.3.3

Apply the distributive property.

$\frac{2 - x \cdot 3 - 3 \cdot 3}{6 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.3.4

Multiply $3$ by $- 1$ .

$\frac{2 - 3 x - 3 \cdot 3}{6 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.3.5

Multiply $- 3$ by $3$ .

$\frac{2 - 3 x - 9}{6 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.4

Subtract $9$ from $2$ .

$\frac{- 3 x - 7}{6 x^{2}} + \frac{1}{6 x^{2}} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 3 x - 7 + 1}{6 x^{2}} = 0$

Step 2.6

Add $- 7$ and $1$ .

$\frac{- 3 x - 6}{6 x^{2}} = 0$

Step 2.7

Cancel the common factor of $- 3 x - 6$ and $6$ .

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Step 2.7.1

Factor $3$ out of $- 3 x$ .

$\frac{3 (- x) - 6}{6 x^{2}} = 0$

Step 2.7.2

Factor $3$ out of $- 6$ .

$\frac{3 (- x) + 3 (- 2)}{6 x^{2}} = 0$

Step 2.7.3

Factor $3$ out of $3 (- x) + 3 (- 2)$ .

$\frac{3 (- x - 2)}{6 x^{2}} = 0$

Step 2.7.4

Cancel the common factors.

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Step 2.7.4.1

Factor $3$ out of $6 x^{2}$ .

$\frac{3 (- x - 2)}{3 (2 x^{2})} = 0$

Step 2.7.4.2

Cancel the common factor.

$\frac{3 (- x - 2)}{3 (2 x^{2})} = 0$

Step 2.7.4.3

Rewrite the expression.

$\frac{- x - 2}{2 x^{2}} = 0$

Step 2.8

Factor $- 1$ out of $- x$ .

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

Step 2.9

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{- (x) - 1 (2)}{2 x^{2}} = 0$

Step 2.10

Factor $- 1$ out of $- (x) - 1 (2)$ .

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

Step 2.11

Rewrite $- (x + 2)$ as $- 1 (x + 2)$ .

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

Step 2.12

Move the negative in front of the fraction.

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

Step 3

Set the numerator equal to zero.

$x + 2 = 0$

Step 4

Subtract $2$ from both sides of the equation.

$x = - 2$