Basic Math Examples

$\frac{3 h - m}{h - 3 m} = F$

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.

$h - 3 m, 1$

Step 1.2

Remove parentheses.

$h - 3 m, 1$

Step 1.3

The LCM of one and any expression is the expression.

$h - 3 m$

Step 2

Multiply each term in $\frac{3 h - m}{h - 3 m} = F$ by $h - 3 m$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{3 h - m}{h - 3 m} = F$ by $h - 3 m$ .

$\frac{3 h - m}{h - 3 m} (h - 3 m) = F (h - 3 m)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $h - 3 m$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 h - m}{h - 3 m} (h - 3 m) = F (h - 3 m)$

Step 2.2.1.2

Rewrite the expression.

$3 h - m = F (h - 3 m)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$3 h - m = F h + F (- 3 m)$

Step 2.3.2

Rewrite using the commutative property of multiplication.

$3 h - m = F h - 3 F m$

Step 3

Solve the equation.

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Step 3.1

Add $3 F m$ to both sides of the equation.

$3 h - m + 3 F m = F h$

Step 3.2

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

$- m + 3 F m = F h - 3 h$

Step 3.3

Factor $m$ out of $- m + 3 F m$ .

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Step 3.3.1

Factor $m$ out of $- m$ .

$m \cdot - 1 + 3 F m = F h - 3 h$

Step 3.3.2

Factor $m$ out of $3 F m$ .

$m \cdot - 1 + m (3 F) = F h - 3 h$

Step 3.3.3

Factor $m$ out of $m \cdot - 1 + m (3 F)$ .

$m (- 1 + 3 F) = F h - 3 h$

Step 3.4

Divide each term in $m (- 1 + 3 F) = F h - 3 h$ by $- 1 + 3 F$ and simplify.

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Step 3.4.1

Divide each term in $m (- 1 + 3 F) = F h - 3 h$ by $- 1 + 3 F$ .

$\frac{m (- 1 + 3 F)}{- 1 + 3 F} = \frac{F h}{- 1 + 3 F} + \frac{- 3 h}{- 1 + 3 F}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $- 1 + 3 F$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{m (- 1 + 3 F)}{- 1 + 3 F} = \frac{F h}{- 1 + 3 F} + \frac{- 3 h}{- 1 + 3 F}$

Step 3.4.2.1.2

Divide $m$ by $1$ .

$m = \frac{F h}{- 1 + 3 F} + \frac{- 3 h}{- 1 + 3 F}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Combine the numerators over the common denominator.

$m = \frac{F h - 3 h}{- 1 + 3 F}$

Step 3.4.3.2

Factor $h$ out of $F h - 3 h$ .

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Step 3.4.3.2.1

Factor $h$ out of $F h$ .

$m = \frac{h F - 3 h}{- 1 + 3 F}$

Step 3.4.3.2.2

Factor $h$ out of $- 3 h$ .

$m = \frac{h F + h \cdot - 3}{- 1 + 3 F}$

Step 3.4.3.2.3

Factor $h$ out of $h F + h \cdot - 3$ .

$m = \frac{h (F - 3)}{- 1 + 3 F}$

Step 3.4.3.3

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

$m = \frac{h (F - 3)}{- 1 (1) + 3 F}$

Step 3.4.3.4

Factor $- 1$ out of $3 F$ .

$m = \frac{h (F - 3)}{- 1 (1) - (- 3 F)}$

Step 3.4.3.5

Factor $- 1$ out of $- 1 (1) - (- 3 F)$ .

$m = \frac{h (F - 3)}{- 1 (1 - 3 F)}$

Step 3.4.3.6

Move the negative in front of the fraction.

$m = - \frac{h (F - 3)}{1 - 3 F}$