Solve for a u=(-2a-3)/(ka) ; for a

$u = \frac{- 2 a - 3}{k a}$ ; for $a$

Step 1

Rewrite the equation as $\frac{- 2 a - 3}{k a} = u$ .

$\frac{- 2 a - 3}{k a} = u$

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.

$k a, 1$

The LCM of one and any expression is the expression.

$k a$

Step 3

Multiply each term in $\frac{- 2 a - 3}{k a} = u$ by $k a$ to eliminate the fractions.

Multiply each term in $\frac{- 2 a - 3}{k a} = u$ by $k a$ .

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

Simplify the left side.

Cancel the common factor of $k a$ .

Cancel the common factor.

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

Rewrite the expression.

$- 2 a - 3 = u (k a)$

Simplify the right side.

Remove parentheses.

$- 2 a - 3 = u k a$

Step 4

Solve the equation.

Subtract $u k a$ from both sides of the equation.

$- 2 a - 3 - u k a = 0$

Add $3$ to both sides of the equation.

$- 2 a - u k a = 3$

Factor $a$ out of $- 2 a - u k a$ .

Factor $a$ out of $- 2 a$ .

$a \cdot - 2 - u k a = 3$

Factor $a$ out of $- u k a$ .

$a \cdot - 2 + a (- u k) = 3$

Factor $a$ out of $a \cdot - 2 + a (- u k)$ .

$a (- 2 - u k) = 3$

Divide each term in $a (- 2 - u k) = 3$ by $- 2 - u k$ and simplify.

Divide each term in $a (- 2 - u k) = 3$ by $- 2 - u k$ .

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

Simplify the left side.

Cancel the common factor of $- 2 - u k$ .

Cancel the common factor.

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

Divide $a$ by $1$ .

$a = \frac{3}{- 2 - u k}$

Simplify the right side.

Rewrite $- 2$ as $- 1 (2)$ .

$a = \frac{3}{- 1 (2) - u k}$

Factor $- 1$ out of $- u k$ .

$a = \frac{3}{- 1 (2) - (u k)}$

Factor $- 1$ out of $- 1 (2) - (u k)$ .

$a = \frac{3}{- 1 (2 + u k)}$

Move the negative in front of the fraction.

$a = - \frac{3}{2 + u k}$

Solve for a u=(-2a-3)/(ka) ; for a

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