Algebra Examples

$- 9 = - \frac{6}{u}$

Step 1

Rewrite the equation as $- \frac{6}{u} = - 9$ .

$- \frac{6}{u} = - 9$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$u, 1$

Step 2.2

The LCM of one and any expression is the expression.

$u$

Step 3

Multiply each term in $- \frac{6}{u} = - 9$ by $u$ to eliminate the fractions.

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Step 3.1

Multiply each term in $- \frac{6}{u} = - 9$ by $u$ .

$- \frac{6}{u} u = - 9 u$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $u$ .

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Step 3.2.1.1

Move the leading negative in $- \frac{6}{u}$ into the numerator.

$\frac{- 6}{u} u = - 9 u$

Step 3.2.1.2

Cancel the common factor.

$\frac{- 6}{u} u = - 9 u$

Step 3.2.1.3

Rewrite the expression.

$- 6 = - 9 u$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $- 9 u = - 6$ .

$- 9 u = - 6$

Step 4.2

Divide each term in $- 9 u = - 6$ by $- 9$ and simplify.

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Step 4.2.1

Divide each term in $- 9 u = - 6$ by $- 9$ .

$\frac{- 9 u}{- 9} = \frac{- 6}{- 9}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 9$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 9 u}{- 9} = \frac{- 6}{- 9}$

Step 4.2.2.1.2

Divide $u$ by $1$ .

$u = \frac{- 6}{- 9}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $- 6$ and $- 9$ .

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Step 4.2.3.1.1

Factor $- 3$ out of $- 6$ .

$u = \frac{- 3 (2)}{- 9}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $- 3$ out of $- 9$ .

$u = \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Step 4.2.3.1.2.2

Cancel the common factor.

$u = \frac{- 3 \cdot 2}{- 3 \cdot 3}$

Step 4.2.3.1.2.3

Rewrite the expression.

$u = \frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$u = \frac{2}{3}$

Decimal Form:

$u = 0.\overline{6}$