Algebra Examples

$\frac{12}{x} + \frac{3}{4} = \frac{3}{2}$

Step 1

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

$\frac{12}{x} + \frac{3}{4} - \frac{3}{2} = 0$

Step 2

Simplify $\frac{12}{x} + \frac{3}{4} - \frac{3}{2}$ .

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Step 2.1

To write $- \frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{12}{x} + \frac{3}{4} - \frac{3}{2} \cdot \frac{2}{2} = 0$

Step 2.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

$\frac{12}{x} + \frac{3}{4} - \frac{3 \cdot 2}{2 \cdot 2} = 0$

Step 2.2.2

Multiply $2$ by $2$ .

$\frac{12}{x} + \frac{3}{4} - \frac{3 \cdot 2}{4} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{12}{x} + \frac{3 - 3 \cdot 2}{4} = 0$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $- 3$ by $2$ .

$\frac{12}{x} + \frac{3 - 6}{4} = 0$

Step 2.4.2

Subtract $6$ from $3$ .

$\frac{12}{x} + \frac{- 3}{4} = 0$

Step 2.5

Move the negative in front of the fraction.

$\frac{12}{x} - \frac{3}{4} = 0$

Step 3

To write $\frac{12}{x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{12}{x} \cdot \frac{4}{4} - \frac{3}{4} = 0$

Step 4

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{12}{x} \cdot \frac{4}{4} - \frac{3}{4} \cdot \frac{x}{x} = 0$

Step 5

Write each expression with a common denominator of $x \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{12}{x}$ by $\frac{4}{4}$ .

$\frac{12 \cdot 4}{x \cdot 4} - \frac{3}{4} \cdot \frac{x}{x} = 0$

Step 5.2

Multiply $\frac{3}{4}$ by $\frac{x}{x}$ .

$\frac{12 \cdot 4}{x \cdot 4} - \frac{3 x}{4 x} = 0$

Step 5.3

Reorder the factors of $x \cdot 4$ .

$\frac{12 \cdot 4}{4 x} - \frac{3 x}{4 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{12 \cdot 4 - 3 x}{4 x} = 0$

Step 7

Simplify the numerator.

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Step 7.1

Factor $3$ out of $12 \cdot 4 - 3 x$ .

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Step 7.1.1

Factor $3$ out of $12 \cdot 4$ .

$\frac{3 (4 \cdot 4) - 3 x}{4 x} = 0$

Step 7.1.2

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

$\frac{3 (4 \cdot 4) + 3 (- x)}{4 x} = 0$

Step 7.1.3

Factor $3$ out of $3 (4 \cdot 4) + 3 (- x)$ .

$\frac{3 (4 \cdot 4 - x)}{4 x} = 0$

Step 7.2

Multiply $4$ by $4$ .

$\frac{3 (16 - x)}{4 x} = 0$

Step 8

Set the numerator equal to zero.

$3 (16 - x) = 0$

Step 9

Solve the equation for $x$ .

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Step 9.1

Divide each term in $3 (16 - x) = 0$ by $3$ and simplify.

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Step 9.1.1

Divide each term in $3 (16 - x) = 0$ by $3$ .

$\frac{3 (16 - x)}{3} = \frac{0}{3}$

Step 9.1.2

Simplify the left side.

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Step 9.1.2.1

Cancel the common factor of $3$ .

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Step 9.1.2.1.1

Cancel the common factor.

$\frac{3 (16 - x)}{3} = \frac{0}{3}$

Step 9.1.2.1.2

Divide $16 - x$ by $1$ .

$16 - x = \frac{0}{3}$

Step 9.1.3

Simplify the right side.

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Step 9.1.3.1

Divide $0$ by $3$ .

$16 - x = 0$

Step 9.2

Subtract $16$ from both sides of the equation.

$- x = - 16$

Step 9.3

Divide each term in $- x = - 16$ by $- 1$ and simplify.

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Step 9.3.1

Divide each term in $- x = - 16$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 16}{- 1}$

Step 9.3.2

Simplify the left side.

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Step 9.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 16}{- 1}$

Step 9.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 16}{- 1}$

Step 9.3.3

Simplify the right side.

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Step 9.3.3.1

Divide $- 16$ by $- 1$ .

$x = 16$