Trigonometry Examples

$x \cdot (1 - y) + 3 y = 3$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x \cdot 1 + x (- y) + 3 y = 3$

Step 1.2

Multiply $x$ by $1$ .

$x + x (- y) + 3 y = 3$

Step 1.3

Rewrite using the commutative property of multiplication.

$x - x y + 3 y = 3$

Step 2

Subtract $3 y$ from both sides of the equation.

$x - x y = 3 - 3 y$

Step 3

Factor $x$ out of $x - x y$ .

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Step 3.1

Factor $x$ out of $x^{1}$ .

$x \cdot 1 - x y = 3 - 3 y$

Step 3.2

Factor $x$ out of $- x y$ .

$x \cdot 1 + x (- 1 y) = 3 - 3 y$

Step 3.3

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

$x (1 - 1 y) = 3 - 3 y$

Step 4

Rewrite $- 1 y$ as $- y$ .

$x (1 - y) = 3 - 3 y$

Step 5

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

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Step 5.1

Divide each term in $x (1 - y) = 3 - 3 y$ by $1 - y$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $1 - y$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{1 - y} + \frac{- 3 y}{1 - y}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Combine the numerators over the common denominator.

$x = \frac{3 - 3 y}{1 - y}$

Step 5.3.2

Factor $3$ out of $3 - 3 y$ .

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Step 5.3.2.1

Factor $3$ out of $3$ .

$x = \frac{3 (1) - 3 y}{1 - y}$

Step 5.3.2.2

Factor $3$ out of $- 3 y$ .

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

Step 5.3.2.3

Factor $3$ out of $3 (1) + 3 (- y)$ .

$x = \frac{3 (1 - y)}{1 - y}$

Step 5.3.3

Cancel the common factor of $1 - y$ .

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Step 5.3.3.1

Cancel the common factor.

$x = \frac{3 (1 - y)}{1 - y}$

Step 5.3.3.2

Divide $3$ by $1$ .

$x = 3$