Pre-Algebra Examples

$\frac{y}{p - q} = \frac{y}{p + q}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$y (p + q) = (p - q) y$

Step 2

Solve the equation for $y$ .

Tap for more steps...

Step 2.1

Simplify $y (p + q)$ .

Tap for more steps...

Step 2.1.1

Rewrite.

$0 + 0 + y (p + q) = (p - q) y$

Step 2.1.2

Simplify by adding zeros.

$y (p + q) = (p - q) y$

Step 2.1.3

Apply the distributive property.

$y p + y q = (p - q) y$

Step 2.2

Apply the distributive property.

$y p + y q = p y - q y$

Step 2.3

Move all terms containing $y$ to the left side of the equation.

Tap for more steps...

Step 2.3.1

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

$y p + y q - p y = - q y$

Step 2.3.2

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

$y p + y q - p y + q y = 0$

Step 2.3.3

Combine the opposite terms in $y p + y q - p y + q y$ .

Tap for more steps...

Step 2.3.3.1

Reorder the factors in the terms $y p$ and $- p y$ .

$p y + y q - p y + q y = 0$

Step 2.3.3.2

Subtract $p y$ from $p y$ .

$y q + 0 + q y = 0$

Step 2.3.3.3

Add $y q$ and $0$ .

$y q + q y = 0$

Step 2.3.4

Add $y q$ and $q y$ .

Tap for more steps...

Step 2.3.4.1

Reorder $y$ and $q$ .

$q y + q y = 0$

Step 2.3.4.2

Add $q y$ and $q y$ .

$2 q y = 0$

Step 2.4

Divide each term in $2 q y = 0$ by $2 q$ and simplify.

Tap for more steps...

Step 2.4.1

Divide each term in $2 q y = 0$ by $2 q$ .

$\frac{2 q y}{2 q} = \frac{0}{2 q}$

Step 2.4.2

Simplify the left side.

Tap for more steps...

Step 2.4.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.2.1.1

Cancel the common factor.

$\frac{2 q y}{2 q} = \frac{0}{2 q}$

Step 2.4.2.1.2

Rewrite the expression.

$\frac{q y}{q} = \frac{0}{2 q}$

Step 2.4.2.2

Cancel the common factor of $q$ .

Tap for more steps...

Step 2.4.2.2.1

Cancel the common factor.

$\frac{q y}{q} = \frac{0}{2 q}$

Step 2.4.2.2.2

Divide $y$ by $1$ .

$y = \frac{0}{2 q}$

Step 2.4.3

Simplify the right side.

Tap for more steps...

Step 2.4.3.1

Cancel the common factor of $0$ and $2$ .

Tap for more steps...

Step 2.4.3.1.1

Factor $2$ out of $0$ .

$y = \frac{2 (0)}{2 q}$

Step 2.4.3.1.2

Cancel the common factors.

Tap for more steps...

Step 2.4.3.1.2.1

Factor $2$ out of $2 q$ .

$y = \frac{2 (0)}{2 (q)}$

Step 2.4.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 0}{2 q}$

Step 2.4.3.1.2.3

Rewrite the expression.

$y = \frac{0}{q}$

Step 2.4.3.2

Divide $0$ by $q$ .

$y = 0$