Solve for y t=(2-3y)/(y+2)

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

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

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

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.

$y + 2, 1$

Remove parentheses.

$y + 2, 1$

The LCM of one and any expression is the expression.

$y + 2$

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

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

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

Simplify the left side.

Cancel the common factor of $y + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$2 - 3 y = t (y + 2)$

Simplify the right side.

Apply the distributive property.

$2 - 3 y = t y + t \cdot 2$

Move $2$ to the left of $t$ .

$2 - 3 y = t y + 2 t$

Solve the equation.

Subtract $t y$ from both sides of the equation.

$2 - 3 y - t y = 2 t$

Subtract $2$ from both sides of the equation.

$- 3 y - t y = 2 t - 2$

Factor $y$ out of $- 3 y - t y$ .

Factor $y$ out of $- 3 y$ .

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

Factor $y$ out of $- t y$ .

$y \cdot - 3 + y (- t) = 2 t - 2$

Factor $y$ out of $y \cdot - 3 + y (- t)$ .

$y (- 3 - t) = 2 t - 2$

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

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

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

Simplify the left side.

Cancel the common factor of $- 3 - t$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Combine the numerators over the common denominator.

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

Factor $2$ out of $2 t - 2$ .

Factor $2$ out of $2 t$ .

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

Factor $2$ out of $- 2$ .

$y = \frac{2 (t) + 2 (- 1)}{- 3 - t}$

Factor $2$ out of $2 (t) + 2 (- 1)$ .

$y = \frac{2 (t - 1)}{- 3 - t}$

Rewrite $- 3$ as $- 1 (3)$ .

$y = \frac{2 (t - 1)}{- 1 (3) - t}$

Factor $- 1$ out of $- t$ .

$y = \frac{2 (t - 1)}{- 1 (3) - (t)}$

Factor $- 1$ out of $- 1 (3) - (t)$ .

$y = \frac{2 (t - 1)}{- 1 (3 + t)}$

Move the negative in front of the fraction.

$y = - \frac{2 (t - 1)}{3 + t}$

Solve for y t=(2-3y)/(y+2)

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