Linear Algebra Examples

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

Step 1

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

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

Step 2

Multiply both sides by $b$ .

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

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $b$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

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

Step 3.1.1.2

Rewrite the expression.

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

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

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

Tap for more steps...

Step 3.2.1.1

Apply the distributive property.

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

Step 3.2.1.2

Multiply $b$ by $1$ .

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

Step 3.2.1.3

Combine $b$ and $\frac{x}{a}$ .

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

Step 3.2.1.4

Reorder $b$ and $- \frac{b x}{a}$ .

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

Step 4

Set the denominator in $\frac{b x}{a}$ equal to $0$ to find where the expression is undefined.

$a = 0$

Step 5

The domain is all values of $b$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${b | b \neq 0}$