Trigonometry Examples

$x a + x b = y c + yd$

Step 1

Factor $x$ out of $x a + x b$ .

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Step 1.1

Factor $x$ out of $x a$ .

$x (a) + x b = y c + yd$

Step 1.2

Factor $x$ out of $x b$ .

$x (a) + x (b) = y c + yd$

Step 1.3

Factor $x$ out of $x (a) + x (b)$ .

$x (a + b) = y c + yd$

Step 2

Divide each term in $x (a + b) = y c + yd$ by $a + b$ and simplify.

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Step 2.1

Divide each term in $x (a + b) = y c + yd$ by $a + b$ .

$\frac{x (a + b)}{a + b} = \frac{y c}{a + b} + \frac{yd}{a + b}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $a + b$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{x (a + b)}{a + b} = \frac{y c}{a + b} + \frac{yd}{a + b}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{y c}{a + b} + \frac{yd}{a + b}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Combine the numerators over the common denominator.

$x = \frac{y c + yd}{a + b}$