Solve for y -6=-9/y

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

Step 1

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

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

Step 2

Find the LCD of the terms in the equation.

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

$y, 1$

The LCM of one and any expression is the expression.

$y$

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $y$ .

Move the leading negative in $- \frac{9}{y}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$- 9 = - 6 y$

Step 4

Solve the equation.

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

$- 6 y = - 9$

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

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

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

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

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

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

$y = \frac{- 3 (3)}{- 6}$

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 1.5$

Mixed Number Form:

$y = 1 \frac{1}{2}$

Solve for y -6=-9/y

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