Trigonometry Examples

$- 3 = \frac{4}{y - 2}$

Step 1

Rewrite the equation as $\frac{4}{y - 2} = - 3$ .

$\frac{4}{y - 2} = - 3$

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.

$y - 2, 1$

Step 2.2

Remove parentheses.

$y - 2, 1$

Step 2.3

The LCM of one and any expression is the expression.

$y - 2$

Step 3

Multiply each term in $\frac{4}{y - 2} = - 3$ by $y - 2$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{4}{y - 2} = - 3$ by $y - 2$ .

$\frac{4}{y - 2} (y - 2) = - 3 (y - 2)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $y - 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4}{y - 2} (y - 2) = - 3 (y - 2)$

Step 3.2.1.2

Rewrite the expression.

$4 = - 3 (y - 2)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$4 = - 3 y - 3 \cdot - 2$

Step 3.3.2

Multiply $- 3$ by $- 2$ .

$4 = - 3 y + 6$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $- 3 y + 6 = 4$ .

$- 3 y + 6 = 4$

Step 4.2

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

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Step 4.2.1

Subtract $6$ from both sides of the equation.

$- 3 y = 4 - 6$

Step 4.2.2

Subtract $6$ from $4$ .

$- 3 y = - 2$

Step 4.3

Divide each term in $- 3 y = - 2$ by $- 3$ and simplify.

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Step 4.3.1

Divide each term in $- 3 y = - 2$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 2}{- 3}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 3$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 2}{- 3}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 2}{- 3}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Dividing two negative values results in a positive value.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 0.\overline{6}$