Basic Math Examples

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

Step 1

Multiply the equation by $p - 2$ .

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

Step 2

Simplify the left side.

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Step 2.1

Apply the distributive property.

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

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $p - 2$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

$p y - 2 y = p + 3$

Step 4

Solve for $p$ .

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Step 4.1

Subtract $p$ from both sides of the equation.

$p y - 2 y - p = 3$

Step 4.2

Add $2 y$ to both sides of the equation.

$p y - p = 3 + 2 y$

Step 4.3

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

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Step 4.3.1

Factor $p$ out of $p y$ .

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

Step 4.3.2

Factor $p$ out of $- p$ .

$p (y) + p \cdot - 1 = 3 + 2 y$

Step 4.3.3

Factor $p$ out of $p (y) + p \cdot - 1$ .

$p (y - 1) = 3 + 2 y$

Step 4.4

Divide each term in $p (y - 1) = 3 + 2 y$ by $y - 1$ and simplify.

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Step 4.4.1

Divide each term in $p (y - 1) = 3 + 2 y$ by $y - 1$ .

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

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $y - 1$ .

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Step 4.4.2.1.1

Cancel the common factor.

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

Step 4.4.2.1.2

Divide $p$ by $1$ .

$p = \frac{3}{y - 1} + \frac{2 y}{y - 1}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Combine the numerators over the common denominator.

$p = \frac{3 + 2 y}{y - 1}$