Solve for n m/n=p-6

$\frac{m}{n} = p - 6$

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.

$n, 1, 1$

The LCM of one and any expression is the expression.

$n$

Step 2

Multiply each term in $\frac{m}{n} = p - 6$ by $n$ to eliminate the fractions.

Multiply each term in $\frac{m}{n} = p - 6$ by $n$ .

$\frac{m}{n} n = p n - 6 n$

Simplify the left side.

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{m}{n} n = p n - 6 n$

Rewrite the expression.

$m = p n - 6 n$

Step 3

Solve the equation.

Rewrite the equation as $p n - 6 n = m$ .

$p n - 6 n = m$

Factor $n$ out of $p n - 6 n$ .

Factor $n$ out of $p n$ .

$n p - 6 n = m$

Factor $n$ out of $- 6 n$ .

$n p + n \cdot - 6 = m$

Factor $n$ out of $n p + n \cdot - 6$ .

$n (p - 6) = m$

Divide each term in $n (p - 6) = m$ by $p - 6$ and simplify.

Divide each term in $n (p - 6) = m$ by $p - 6$ .

$\frac{n (p - 6)}{p - 6} = \frac{m}{p - 6}$

Simplify the left side.

Cancel the common factor of $p - 6$ .

Cancel the common factor.

$\frac{n (p - 6)}{p - 6} = \frac{m}{p - 6}$

Divide $n$ by $1$ .

$n = \frac{m}{p - 6}$