Basic Math Examples

$5 - \frac{2}{3 h} = 2 a + a \cdot - 1$

Step 1

Simplify $2 a + a \cdot - 1$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Move $- 1$ to the left of $a$ .

$5 - \frac{2}{3 h} = 2 a - 1 \cdot a$

Step 1.1.2

Rewrite $- 1 a$ as $- a$ .

$5 - \frac{2}{3 h} = 2 a - a$

Step 1.2

Subtract $a$ from $2 a$ .

$5 - \frac{2}{3 h} = a$

Step 2

Subtract $5$ from both sides of the equation.

$- \frac{2}{3 h} = a - 5$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 h, 1, 1$

Step 3.2

The LCM of one and any expression is the expression.

$3 h$

Step 4

Multiply each term in $- \frac{2}{3 h} = a - 5$ by $3 h$ to eliminate the fractions.

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Step 4.1

Multiply each term in $- \frac{2}{3 h} = a - 5$ by $3 h$ .

$- \frac{2}{3 h} (3 h) = a (3 h) - 5 (3 h)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3 h$ .

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Step 4.2.1.1

Move the leading negative in $- \frac{2}{3 h}$ into the numerator.

$\frac{- 2}{3 h} (3 h) = a (3 h) - 5 (3 h)$

Step 4.2.1.2

Cancel the common factor.

$\frac{- 2}{3 h} (3 h) = a (3 h) - 5 (3 h)$

Step 4.2.1.3

Rewrite the expression.

$- 2 = a (3 h) - 5 (3 h)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Rewrite using the commutative property of multiplication.

$- 2 = 3 a h - 5 (3 h)$

Step 4.3.1.2

Multiply $3$ by $- 5$ .

$- 2 = 3 a h - 15 h$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $3 a h - 15 h = - 2$ .

$3 a h - 15 h = - 2$

Step 5.2

Factor $3 h$ out of $3 a h - 15 h$ .

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Step 5.2.1

Factor $3 h$ out of $3 a h$ .

$3 h (a) - 15 h = - 2$

Step 5.2.2

Factor $3 h$ out of $- 15 h$ .

$3 h (a) + 3 h (- 5) = - 2$

Step 5.2.3

Factor $3 h$ out of $3 h (a) + 3 h (- 5)$ .

$3 h (a - 5) = - 2$

Step 5.3

Divide each term in $3 h (a - 5) = - 2$ by $3 (a - 5)$ and simplify.

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Step 5.3.1

Divide each term in $3 h (a - 5) = - 2$ by $3 (a - 5)$ .

$\frac{3 h (a - 5)}{3 (a - 5)} = \frac{- 2}{3 (a - 5)}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $3$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{3 h (a - 5)}{3 (a - 5)} = \frac{- 2}{3 (a - 5)}$

Step 5.3.2.1.2

Rewrite the expression.

$\frac{h (a - 5)}{a - 5} = \frac{- 2}{3 (a - 5)}$

Step 5.3.2.2

Cancel the common factor of $a - 5$ .

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Step 5.3.2.2.1

Cancel the common factor.

$\frac{h (a - 5)}{a - 5} = \frac{- 2}{3 (a - 5)}$

Step 5.3.2.2.2

Divide $h$ by $1$ .

$h = \frac{- 2}{3 (a - 5)}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Move the negative in front of the fraction.

$h = - \frac{2}{3 (a - 5)}$