Basic Math Examples

$\frac{12 e}{5} = \frac{1}{8 f} + \frac{1}{9 g} \cdot \frac{h}{j}$

Step 1

Rewrite the equation as $\frac{1}{8 f} + \frac{1}{9 g} \cdot \frac{h}{j} = \frac{12 e}{5}$ .

$\frac{1}{8 f} + \frac{1}{9 g} \cdot \frac{h}{j} = \frac{12 e}{5}$

Step 2

Multiply $\frac{1}{9 g}$ by $\frac{h}{j}$ .

$\frac{1}{8 f} + \frac{h}{9 g j} = \frac{12 e}{5}$

Step 3

Subtract $\frac{1}{8 f}$ from both sides of the equation.

$\frac{h}{9 g j} = \frac{12 e}{5} - \frac{1}{8 f}$

Step 4

Multiply both sides by $9 g j$ .

$\frac{h}{9 g j} (9 g j) = (\frac{12 e}{5} - \frac{1}{8 f}) (9 g j)$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{h}{9 g j} (9 g j)$ .

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Step 5.1.1.1

Rewrite using the commutative property of multiplication.

$9 \frac{h}{9 g j} (g j) = (\frac{12 e}{5} - \frac{1}{8 f}) (9 g j)$

Step 5.1.1.2

Cancel the common factor of $9$ .

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Step 5.1.1.2.1

Factor $9$ out of $9 g j$ .

$9 \frac{h}{9 (g j)} (g j) = (\frac{12 e}{5} - \frac{1}{8 f}) (9 g j)$

Step 5.1.1.2.2

Cancel the common factor.

$9 \frac{h}{9 (g j)} (g j) = (\frac{12 e}{5} - \frac{1}{8 f}) (9 g j)$

Step 5.1.1.2.3

Rewrite the expression.

$\frac{h}{g j} (g j) = (\frac{12 e}{5} - \frac{1}{8 f}) (9 g j)$

Step 5.1.1.3

Cancel the common factor of $g j$ .

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Step 5.1.1.3.1

Cancel the common factor.

$\frac{h}{g j} (g j) = (\frac{12 e}{5} - \frac{1}{8 f}) (9 g j)$

Step 5.1.1.3.2

Rewrite the expression.

$h = (\frac{12 e}{5} - \frac{1}{8 f}) (9 g j)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $(\frac{12 e}{5} - \frac{1}{8 f}) (9 g j)$ .

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Step 5.2.1.1

Apply the distributive property.

$h = \frac{12 e}{5} (9 g j) - \frac{1}{8 f} (9 g j)$

Step 5.2.1.2

Multiply $\frac{12 e}{5} (9 g j)$ .

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Step 5.2.1.2.1

Combine $9$ and $\frac{12 e}{5}$ .

$h = \frac{9 (12 e)}{5} (g j) - \frac{1}{8 f} (9 g j)$

Step 5.2.1.2.2

Multiply $12$ by $9$ .

$h = \frac{108 e}{5} (g j) - \frac{1}{8 f} (9 g j)$

Step 5.2.1.2.3

Combine $g$ and $\frac{108 e}{5}$ .

$h = \frac{g (108 e)}{5} j - \frac{1}{8 f} (9 g j)$

Step 5.2.1.2.4

Combine $\frac{g (108 e)}{5}$ and $j$ .

$h = \frac{g (108 e) j}{5} - \frac{1}{8 f} (9 g j)$

Step 5.2.1.3

Multiply $- \frac{1}{8 f} (9 g j)$ .

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Step 5.2.1.3.1

Multiply $9$ by $- 1$ .

$h = \frac{g (108 e) j}{5} - 9 \frac{1}{8 f} (g j)$

Step 5.2.1.3.2

Combine $- 9$ and $\frac{1}{8 f}$ .

$h = \frac{g (108 e) j}{5} + \frac{- 9}{8 f} (g j)$

Step 5.2.1.3.3

Combine $g$ and $\frac{- 9}{8 f}$ .

$h = \frac{g (108 e) j}{5} + \frac{g \cdot - 9}{8 f} j$

Step 5.2.1.3.4

Combine $\frac{g \cdot - 9}{8 f}$ and $j$ .

$h = \frac{g (108 e) j}{5} + \frac{g \cdot - 9 j}{8 f}$

Step 5.2.1.4

Simplify each term.

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Step 5.2.1.4.1

Move $108$ to the left of $g$ .

$h = \frac{108 \cdot g e j}{5} + \frac{g \cdot - 9 j}{8 f}$

Step 5.2.1.4.2

Move $- 9$ to the left of $g$ .

$h = \frac{108 g e j}{5} + \frac{- 9 \cdot g j}{8 f}$

Step 5.2.1.4.3

Move the negative in front of the fraction.

$h = \frac{108 g e j}{5} - \frac{9 g j}{8 f}$

Step 5.2.1.5

Move $e$ .

$h = \frac{108 g j e}{5} - \frac{9 g j}{8 f}$