Solve for n (n+4)/(n-6)=7s

$\frac{n + 4}{n - 6} = 7 s$

Step 1

Find the LCD of the terms in the equation.

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

$n - 6, 1$

Remove parentheses.

$n - 6, 1$

The LCM of one and any expression is the expression.

$n - 6$

Step 2

Multiply each term in $\frac{n + 4}{n - 6} = 7 s$ by $n - 6$ to eliminate the fractions.

Multiply each term in $\frac{n + 4}{n - 6} = 7 s$ by $n - 6$ .

$\frac{n + 4}{n - 6} (n - 6) = 7 s (n - 6)$

Simplify the left side.

Cancel the common factor of $n - 6$ .

Cancel the common factor.

$\frac{n + 4}{n - 6} (n - 6) = 7 s (n - 6)$

Rewrite the expression.

$n + 4 = 7 s (n - 6)$

Simplify the right side.

Apply the distributive property.

$n + 4 = 7 s n + 7 s \cdot - 6$

Multiply $- 6$ by $7$ .

$n + 4 = 7 s n - 42 s$

Step 3

Solve the equation.

Subtract $7 s n$ from both sides of the equation.

$n + 4 - 7 s n = - 42 s$

Subtract $4$ from both sides of the equation.

$n - 7 s n = - 42 s - 4$

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

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

$n \cdot 1 - 7 s n = - 42 s - 4$

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

$n \cdot 1 + n (- 7 s) = - 42 s - 4$

Factor $n$ out of $n \cdot 1 + n (- 7 s)$ .

$n (1 - 7 s) = - 42 s - 4$

Divide each term in $n (1 - 7 s) = - 42 s - 4$ by $1 - 7 s$ and simplify.

Divide each term in $n (1 - 7 s) = - 42 s - 4$ by $1 - 7 s$ .

$\frac{n (1 - 7 s)}{1 - 7 s} = \frac{- 42 s}{1 - 7 s} + \frac{- 4}{1 - 7 s}$

Simplify the left side.

Cancel the common factor of $1 - 7 s$ .

Cancel the common factor.

$\frac{n (1 - 7 s)}{1 - 7 s} = \frac{- 42 s}{1 - 7 s} + \frac{- 4}{1 - 7 s}$

Divide $n$ by $1$ .

$n = \frac{- 42 s}{1 - 7 s} + \frac{- 4}{1 - 7 s}$

Simplify the right side.

Combine the numerators over the common denominator.

$n = \frac{- 42 s - 4}{1 - 7 s}$

Factor $2$ out of $- 42 s - 4$ .

Factor $2$ out of $- 42 s$ .

$n = \frac{2 (- 21 s) - 4}{1 - 7 s}$

Factor $2$ out of $- 4$ .

$n = \frac{2 (- 21 s) + 2 (- 2)}{1 - 7 s}$

Factor $2$ out of $2 (- 21 s) + 2 (- 2)$ .

$n = \frac{2 (- 21 s - 2)}{1 - 7 s}$

Factor $- 1$ out of $- 21 s$ .

$n = \frac{2 (- (21 s) - 2)}{1 - 7 s}$

Rewrite $- 2$ as $- 1 (2)$ .

$n = \frac{2 (- (21 s) - 1 (2))}{1 - 7 s}$

Factor $- 1$ out of $- (21 s) - 1 (2)$ .

$n = \frac{2 (- (21 s + 2))}{1 - 7 s}$

Simplify the expression.

Rewrite $- (21 s + 2)$ as $- 1 (21 s + 2)$ .

$n = \frac{2 (- 1 (21 s + 2))}{1 - 7 s}$

Move the negative in front of the fraction.

$n = - \frac{2 (21 s + 2)}{1 - 7 s}$

Solve for n (n+4)/(n-6)=7s

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