Basic Math Examples

$\frac{m - n}{r n} = t$

Step 1

Find the LCD of the terms in the equation.

Tap for more steps...

Step 1.1

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

$r n, 1$

Step 1.2

The LCM of one and any expression is the expression.

$r n$

Step 2

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

Tap for more steps...

Step 2.1

Multiply each term in $\frac{m - n}{r n} = t$ by $r n$ .

$\frac{m - n}{r n} (r n) = t (r n)$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $r n$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{m - n}{r n} (r n) = t (r n)$

Step 2.2.1.2

Rewrite the expression.

$m - n = t (r n)$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Remove parentheses.

$m - n = t r n$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

Subtract $t r n$ from both sides of the equation.

$m - n - t r n = 0$

Step 3.2

Subtract $m$ from both sides of the equation.

$- n - t r n = - m$

Step 3.3

Factor $n$ out of $- n - t r n$ .

Tap for more steps...

Step 3.3.1

Factor $n$ out of $- n$ .

$n \cdot - 1 - t r n = - m$

Step 3.3.2

Factor $n$ out of $- t r n$ .

$n \cdot - 1 + n (- t r) = - m$

Step 3.3.3

Factor $n$ out of $n \cdot - 1 + n (- t r)$ .

$n (- 1 - t r) = - m$

Step 3.4

Divide each term in $n (- 1 - t r) = - m$ by $- 1 - t r$ and simplify.

Tap for more steps...

Step 3.4.1

Divide each term in $n (- 1 - t r) = - m$ by $- 1 - t r$ .

$\frac{n (- 1 - t r)}{- 1 - t r} = \frac{- m}{- 1 - t r}$

Step 3.4.2

Simplify the left side.

Tap for more steps...

Step 3.4.2.1

Cancel the common factor of $- 1 - t r$ .

Tap for more steps...

Step 3.4.2.1.1

Cancel the common factor.

$\frac{n (- 1 - t r)}{- 1 - t r} = \frac{- m}{- 1 - t r}$

Step 3.4.2.1.2

Divide $n$ by $1$ .

$n = \frac{- m}{- 1 - t r}$

Step 3.4.3

Simplify the right side.

Tap for more steps...

Step 3.4.3.1

Move the negative in front of the fraction.

$n = - \frac{m}{- 1 - t r}$

Step 3.4.3.2

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

$n = - \frac{m}{- 1 (1) - t r}$

Step 3.4.3.3

Factor $- 1$ out of $- t r$ .

$n = - \frac{m}{- 1 (1) - (t r)}$

Step 3.4.3.4

Factor $- 1$ out of $- 1 (1) - (t r)$ .

$n = - \frac{m}{- 1 (1 + t r)}$

Step 3.4.3.5

Simplify the expression.

Tap for more steps...

Step 3.4.3.5.1

Move the negative in front of the fraction.

$n = - - \frac{m}{1 + t r}$

Step 3.4.3.5.2

Multiply $- 1$ by $- 1$ .

$n = 1 \frac{m}{1 + t r}$

Step 3.4.3.5.3

Multiply $\frac{m}{1 + t r}$ by $1$ .

$n = \frac{m}{1 + t r}$