Basic Math Examples

$\frac{2 g}{3 h} - \frac{h - 1}{6} = - \frac{2}{h}$

Step 1

Move all terms containing variables to the left side of the equation.

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Step 1.1

Add $\frac{2}{h}$ to both sides of the equation.

$\frac{2 g}{3 h} - \frac{h - 1}{6} + \frac{2}{h} = 0$

Step 1.2

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

$\frac{2 g}{3 h} \cdot \frac{2}{2} - \frac{h - 1}{6} + \frac{2}{h} = 0$

Step 1.3

To write $- \frac{h - 1}{6}$ as a fraction with a common denominator, multiply by $\frac{h}{h}$ .

$\frac{2 g}{3 h} \cdot \frac{2}{2} - \frac{h - 1}{6} \cdot \frac{h}{h} + \frac{2}{h} = 0$

Step 1.4

Write each expression with a common denominator of $6 h$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

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

$\frac{2 g \cdot 2}{3 h \cdot 2} - \frac{h - 1}{6} \cdot \frac{h}{h} + \frac{2}{h} = 0$

Step 1.4.2

Multiply $2$ by $3$ .

$\frac{2 g \cdot 2}{6 h} - \frac{h - 1}{6} \cdot \frac{h}{h} + \frac{2}{h} = 0$

Step 1.4.3

Multiply $\frac{h - 1}{6}$ by $\frac{h}{h}$ .

$\frac{2 g \cdot 2}{6 h} - \frac{(h - 1) h}{6 h} + \frac{2}{h} = 0$

Step 1.5

Combine the numerators over the common denominator.

$\frac{2 g \cdot 2 - (h - 1) h}{6 h} + \frac{2}{h} = 0$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $2$ by $2$ .

$\frac{4 g - (h - 1) h}{6 h} + \frac{2}{h} = 0$

Step 1.6.2

Apply the distributive property.

$\frac{4 g + (- h - - 1) h}{6 h} + \frac{2}{h} = 0$

Step 1.6.3

Multiply $- 1$ by $- 1$ .

$\frac{4 g + (- h + 1) h}{6 h} + \frac{2}{h} = 0$

Step 1.6.4

Apply the distributive property.

$\frac{4 g - h \cdot h + 1 h}{6 h} + \frac{2}{h} = 0$

Step 1.6.5

Multiply $h$ by $h$ by adding the exponents.

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Step 1.6.5.1

Move $h$ .

$\frac{4 g - (h \cdot h) + 1 h}{6 h} + \frac{2}{h} = 0$

Step 1.6.5.2

Multiply $h$ by $h$ .

$\frac{4 g - h^{2} + 1 h}{6 h} + \frac{2}{h} = 0$

Step 1.6.6

Multiply $h$ by $1$ .

$\frac{4 g - h^{2} + h}{6 h} + \frac{2}{h} = 0$

Step 1.7

To write $\frac{2}{h}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{4 g - h^{2} + h}{6 h} + \frac{2}{h} \cdot \frac{6}{6} = 0$

Step 1.8

Write each expression with a common denominator of $6 h$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.8.1

Multiply $\frac{2}{h}$ by $\frac{6}{6}$ .

$\frac{4 g - h^{2} + h}{6 h} + \frac{2 \cdot 6}{h \cdot 6} = 0$

Step 1.8.2

Reorder the factors of $h \cdot 6$ .

$\frac{4 g - h^{2} + h}{6 h} + \frac{2 \cdot 6}{6 h} = 0$

Step 1.9

Combine the numerators over the common denominator.

$\frac{4 g - h^{2} + h + 2 \cdot 6}{6 h} = 0$

Step 1.10

Multiply $2$ by $6$ .

$\frac{4 g - h^{2} + h + 12}{6 h} = 0$

Step 2

Set the numerator equal to zero.

$4 g - h^{2} + h + 12 = 0$

Step 3

Solve the equation for $g$ .

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Step 3.1

Move all terms not containing $g$ to the right side of the equation.

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Step 3.1.1

Add $h^{2}$ to both sides of the equation.

$4 g + h + 12 = h^{2}$

Step 3.1.2

Subtract $h$ from both sides of the equation.

$4 g + 12 = h^{2} - h$

Step 3.1.3

Subtract $12$ from both sides of the equation.

$4 g = h^{2} - h - 12$

Step 3.2

Divide each term in $4 g = h^{2} - h - 12$ by $4$ and simplify.

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Step 3.2.1

Divide each term in $4 g = h^{2} - h - 12$ by $4$ .

$\frac{4 g}{4} = \frac{h^{2}}{4} + \frac{- h}{4} + \frac{- 12}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 g}{4} = \frac{h^{2}}{4} + \frac{- h}{4} + \frac{- 12}{4}$

Step 3.2.2.1.2

Divide $g$ by $1$ .

$g = \frac{h^{2}}{4} + \frac{- h}{4} + \frac{- 12}{4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Move the negative in front of the fraction.

$g = \frac{h^{2}}{4} - \frac{h}{4} + \frac{- 12}{4}$

Step 3.2.3.1.2

Divide $- 12$ by $4$ .

$g = \frac{h^{2}}{4} - \frac{h}{4} - 3$