Algebra Examples

$\frac{n + 6}{n - 7} = 2 s$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

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

$n - 7, 1$

Step 1.2

Remove parentheses.

$n - 7, 1$

Step 1.3

The LCM of one and any expression is the expression.

$n - 7$

Step 2

Multiply each term in $\frac{n + 6}{n - 7} = 2 s$ by $n - 7$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{n + 6}{n - 7} = 2 s$ by $n - 7$ .

$\frac{n + 6}{n - 7} (n - 7) = 2 s (n - 7)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $n - 7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{n + 6}{n - 7} (n - 7) = 2 s (n - 7)$

Step 2.2.1.2

Rewrite the expression.

$n + 6 = 2 s (n - 7)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$n + 6 = 2 s n + 2 s \cdot - 7$

Step 2.3.2

Multiply $- 7$ by $2$ .

$n + 6 = 2 s n - 14 s$

Step 3

Solve the equation.

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Step 3.1

Subtract $2 s n$ from both sides of the equation.

$n + 6 - 2 s n = - 14 s$

Step 3.2

Subtract $6$ from both sides of the equation.

$n - 2 s n = - 14 s - 6$

Step 3.3

Factor $n$ out of $n - 2 s n$ .

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Step 3.3.1

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

$n \cdot 1 - 2 s n = - 14 s - 6$

Step 3.3.2

Factor $n$ out of $- 2 s n$ .

$n \cdot 1 + n (- 2 s) = - 14 s - 6$

Step 3.3.3

Factor $n$ out of $n \cdot 1 + n (- 2 s)$ .

$n (1 - 2 s) = - 14 s - 6$

Step 3.4

Divide each term in $n (1 - 2 s) = - 14 s - 6$ by $1 - 2 s$ and simplify.

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Step 3.4.1

Divide each term in $n (1 - 2 s) = - 14 s - 6$ by $1 - 2 s$ .

$\frac{n (1 - 2 s)}{1 - 2 s} = \frac{- 14 s}{1 - 2 s} + \frac{- 6}{1 - 2 s}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $1 - 2 s$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{n (1 - 2 s)}{1 - 2 s} = \frac{- 14 s}{1 - 2 s} + \frac{- 6}{1 - 2 s}$

Step 3.4.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 14 s}{1 - 2 s} + \frac{- 6}{1 - 2 s}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Combine the numerators over the common denominator.

$n = \frac{- 14 s - 6}{1 - 2 s}$

Step 3.4.3.2

Factor $2$ out of $- 14 s - 6$ .

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Step 3.4.3.2.1

Factor $2$ out of $- 14 s$ .

$n = \frac{2 (- 7 s) - 6}{1 - 2 s}$

Step 3.4.3.2.2

Factor $2$ out of $- 6$ .

$n = \frac{2 (- 7 s) + 2 (- 3)}{1 - 2 s}$

Step 3.4.3.2.3

Factor $2$ out of $2 (- 7 s) + 2 (- 3)$ .

$n = \frac{2 (- 7 s - 3)}{1 - 2 s}$

Step 3.4.3.3

Factor $- 1$ out of $- 7 s$ .

$n = \frac{2 (- (7 s) - 3)}{1 - 2 s}$

Step 3.4.3.4

Rewrite $- 3$ as $- 1 (3)$ .

$n = \frac{2 (- (7 s) - 1 (3))}{1 - 2 s}$

Step 3.4.3.5

Factor $- 1$ out of $- (7 s) - 1 (3)$ .

$n = \frac{2 (- (7 s + 3))}{1 - 2 s}$

Step 3.4.3.6

Simplify the expression.

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Step 3.4.3.6.1

Rewrite $- (7 s + 3)$ as $- 1 (7 s + 3)$ .

$n = \frac{2 (- 1 (7 s + 3))}{1 - 2 s}$

Step 3.4.3.6.2

Move the negative in front of the fraction.

$n = - \frac{2 (7 s + 3)}{1 - 2 s}$