Trigonometry Examples

$\frac{6}{2} = \frac{b + 3}{b - 7}$

Step 1

Rewrite the equation as $\frac{b + 3}{b - 7} = \frac{6}{2}$ .

$\frac{b + 3}{b - 7} = \frac{6}{2}$

Step 2

Divide $6$ by $2$ .

$\frac{b + 3}{b - 7} = 3$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$b - 7, 1$

Step 3.2

Remove parentheses.

$b - 7, 1$

Step 3.3

The LCM of one and any expression is the expression.

$b - 7$

Step 4

Multiply each term in $\frac{b + 3}{b - 7} = 3$ by $b - 7$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{b + 3}{b - 7} = 3$ by $b - 7$ .

$\frac{b + 3}{b - 7} (b - 7) = 3 (b - 7)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $b - 7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{b + 3}{b - 7} (b - 7) = 3 (b - 7)$

Step 4.2.1.2

Rewrite the expression.

$b + 3 = 3 (b - 7)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Apply the distributive property.

$b + 3 = 3 b + 3 \cdot - 7$

Step 4.3.2

Multiply $3$ by $- 7$ .

$b + 3 = 3 b - 21$

Step 5

Solve the equation.

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Step 5.1

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

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Step 5.1.1

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

$b + 3 - 3 b = - 21$

Step 5.1.2

Subtract $3 b$ from $b$ .

$- 2 b + 3 = - 21$

Step 5.2

Move all terms not containing $b$ to the right side of the equation.

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Step 5.2.1

Subtract $3$ from both sides of the equation.

$- 2 b = - 21 - 3$

Step 5.2.2

Subtract $3$ from $- 21$ .

$- 2 b = - 24$

Step 5.3

Divide each term in $- 2 b = - 24$ by $- 2$ and simplify.

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Step 5.3.1

Divide each term in $- 2 b = - 24$ by $- 2$ .

$\frac{- 2 b}{- 2} = \frac{- 24}{- 2}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $- 2$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{- 2 b}{- 2} = \frac{- 24}{- 2}$

Step 5.3.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 24}{- 2}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Divide $- 24$ by $- 2$ .

$b = 12$