Basic Math Examples

$- 6 y = 6 y^{- 1}$

Step 1

Simplify $6 y^{- 1}$ .

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- 6 y = 6 \frac{1}{y}$

Step 1.2

Combine $6$ and $\frac{1}{y}$ .

$- 6 y = \frac{6}{y}$

Step 2

Subtract $\frac{6}{y}$ from both sides of the equation.

$- 6 y - \frac{6}{y} = 0$

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.

$1, y, 1$

Step 3.2

The LCM of one and any expression is the expression.

$y$

Step 4

Multiply each term in $- 6 y - \frac{6}{y} = 0$ by $y$ to eliminate the fractions.

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Step 4.1

Multiply each term in $- 6 y - \frac{6}{y} = 0$ by $y$ .

$- 6 y \cdot y - \frac{6}{y} y = 0 y$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

Multiply $y$ by $y$ by adding the exponents.

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Step 4.2.1.1.1

Move $y$ .

$- 6 (y \cdot y) - \frac{6}{y} y = 0 y$

Step 4.2.1.1.2

Multiply $y$ by $y$ .

$- 6 y^{2} - \frac{6}{y} y = 0 y$

Step 4.2.1.2

Cancel the common factor of $y$ .

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Step 4.2.1.2.1

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

$- 6 y^{2} + \frac{- 6}{y} y = 0 y$

Step 4.2.1.2.2

Cancel the common factor.

$- 6 y^{2} + \frac{- 6}{y} y = 0 y$

Step 4.2.1.2.3

Rewrite the expression.

$- 6 y^{2} - 6 = 0 y$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply $0$ by $y$ .

$- 6 y^{2} - 6 = 0$

Step 5

Solve the equation.

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Step 5.1

Add $6$ to both sides of the equation.

$- 6 y^{2} = 6$

Step 5.2

Divide each term in $- 6 y^{2} = 6$ by $- 6$ and simplify.

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Step 5.2.1

Divide each term in $- 6 y^{2} = 6$ by $- 6$ .

$\frac{- 6 y^{2}}{- 6} = \frac{6}{- 6}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $- 6$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{- 6 y^{2}}{- 6} = \frac{6}{- 6}$

Step 5.2.2.1.2

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{6}{- 6}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $6$ by $- 6$ .

$y^{2} = - 1$

Step 5.3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{- 1}$

Step 5.4

Rewrite $\sqrt{- 1}$ as $i$ .

$y = \pm i$

Step 5.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.5.1

First, use the positive value of the $\pm$ to find the first solution.

$y = i$

Step 5.5.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - i$

Step 5.5.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = i, - i$