Pre-Algebra Examples

$\frac{x}{a} + \frac{y}{a} = 1$

Step 1

Subtract $\frac{y}{a}$ from both sides of the equation.

$\frac{x}{a} = 1 - \frac{y}{a}$

Step 2

Multiply both sides by $a$ .

$\frac{x}{a} a = (1 - \frac{y}{a}) a$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $a$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{x}{a} a = (1 - \frac{y}{a}) a$

Step 3.1.1.2

Rewrite the expression.

$x = (1 - \frac{y}{a}) a$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $(1 - \frac{y}{a}) a$ .

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Step 3.2.1.1

Apply the distributive property.

$x = 1 a - \frac{y}{a} a$

Step 3.2.1.2

Multiply $a$ by $1$ .

$x = a - \frac{y}{a} a$

Step 3.2.1.3

Cancel the common factor of $a$ .

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Step 3.2.1.3.1

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

$x = a + \frac{- y}{a} a$

Step 3.2.1.3.2

Cancel the common factor.

$x = a + \frac{- y}{a} a$

Step 3.2.1.3.3

Rewrite the expression.

$x = a - y$