Basic Math Examples

$\frac{a - 4 b}{- 2 a + 4 b} = - 8$

Step 1

Factor $2$ out of $- 2 a + 4 b$ .

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Step 1.1

Factor $2$ out of $- 2 a$ .

$\frac{a - 4 b}{2 (- a) + 4 b} = - 8$

Step 1.2

Factor $2$ out of $4 b$ .

$\frac{a - 4 b}{2 (- a) + 2 (2 b)} = - 8$

Step 1.3

Factor $2$ out of $2 (- a) + 2 (2 b)$ .

$\frac{a - 4 b}{2 (- a + 2 b)} = - 8$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$2 (- a + 2 b), 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 (- a + 2 b)$

Step 3

Multiply each term in $\frac{a - 4 b}{2 (- a + 2 b)} = - 8$ by $2 (- a + 2 b)$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{a - 4 b}{2 (- a + 2 b)} = - 8$ by $2 (- a + 2 b)$ .

$\frac{a - 4 b}{2 (- a + 2 b)} (2 (- a + 2 b)) = - 8 (2 (- a + 2 b))$

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$2 \frac{a - 4 b}{2 (- a + 2 b)} (- a + 2 b) = - 8 (2 (- a + 2 b))$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Cancel the common factor.

$2 \frac{a - 4 b}{2 (- a + 2 b)} (- a + 2 b) = - 8 (2 (- a + 2 b))$

Step 3.2.2.2

Rewrite the expression.

$\frac{a - 4 b}{- a + 2 b} (- a + 2 b) = - 8 (2 (- a + 2 b))$

Step 3.2.3

Multiply $\frac{a - 4 b}{- a + 2 b}$ by $- a + 2 b$ .

$\frac{(a - 4 b) (- a + 2 b)}{- a + 2 b} = - 8 (2 (- a + 2 b))$

Step 3.2.4

Cancel the common factor of $- a + 2 b$ .

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Step 3.2.4.1

Cancel the common factor.

$\frac{(a - 4 b) (- a + 2 b)}{- a + 2 b} = - 8 (2 (- a + 2 b))$

Step 3.2.4.2

Divide $a - 4 b$ by $1$ .

$a - 4 b = - 8 (2 (- a + 2 b))$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$a - 4 b = - 8 (2 (- a) + 2 (2 b))$

Step 3.3.2

Multiply.

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Step 3.3.2.1

Multiply $- 1$ by $2$ .

$a - 4 b = - 8 (- 2 a + 2 (2 b))$

Step 3.3.2.2

Multiply $2$ by $2$ .

$a - 4 b = - 8 (- 2 a + 4 b)$

Step 3.3.3

Apply the distributive property.

$a - 4 b = - 8 (- 2 a) - 8 (4 b)$

Step 3.3.4

Multiply.

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Step 3.3.4.1

Multiply $- 2$ by $- 8$ .

$a - 4 b = 16 a - 8 (4 b)$

Step 3.3.4.2

Multiply $4$ by $- 8$ .

$a - 4 b = 16 a - 32 b$

Step 4

Solve the equation.

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Step 4.1

Move all terms containing $a$ to the left side of the equation.

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Step 4.1.1

Subtract $16 a$ from both sides of the equation.

$a - 4 b - 16 a = - 32 b$

Step 4.1.2

Subtract $16 a$ from $a$ .

$- 15 a - 4 b = - 32 b$

Step 4.2

Move all terms not containing $a$ to the right side of the equation.

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Step 4.2.1

Add $4 b$ to both sides of the equation.

$- 15 a = - 32 b + 4 b$

Step 4.2.2

Add $- 32 b$ and $4 b$ .

$- 15 a = - 28 b$

Step 4.3

Divide each term in $- 15 a = - 28 b$ by $- 15$ and simplify.

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Step 4.3.1

Divide each term in $- 15 a = - 28 b$ by $- 15$ .

$\frac{- 15 a}{- 15} = \frac{- 28 b}{- 15}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 15$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 15 a}{- 15} = \frac{- 28 b}{- 15}$

Step 4.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 28 b}{- 15}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Dividing two negative values results in a positive value.

$a = \frac{28 b}{15}$