Basic Math Examples

$k = p - \frac{3 t}{y}$

Step 1

Rewrite the equation as $p - \frac{3 t}{y} = k$ .

$p - \frac{3 t}{y} = k$

Step 2

Subtract $p$ from both sides of the equation.

$- \frac{3 t}{y} = k - p$

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.

$y, 1, 1$

Step 3.2

The LCM of one and any expression is the expression.

$y$

Step 4

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

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Step 4.1

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

$- \frac{3 t}{y} y = k y - p y$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $y$ .

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Step 4.2.1.1

Move the leading negative in $- \frac{3 t}{y}$ into the numerator.

$\frac{- 3 t}{y} y = k y - p y$

Step 4.2.1.2

Cancel the common factor.

$\frac{- 3 t}{y} y = k y - p y$

Step 4.2.1.3

Rewrite the expression.

$- 3 t = k y - p y$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $k y - p y = - 3 t$ .

$k y - p y = - 3 t$

Step 5.2

Factor $y$ out of $k y - p y$ .

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Step 5.2.1

Factor $y$ out of $k y$ .

$y k - p y = - 3 t$

Step 5.2.2

Factor $y$ out of $- p y$ .

$y k + y (- p) = - 3 t$

Step 5.2.3

Factor $y$ out of $y k + y (- p)$ .

$y (k - p) = - 3 t$

Step 5.3

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

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Step 5.3.1

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

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

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $k - p$ .

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Step 5.3.2.1.1

Cancel the common factor.

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

Step 5.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 3 t}{k - p}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Move the negative in front of the fraction.

$y = - \frac{3 t}{k - p}$