Basic Math Examples

$8 = \frac{a}{a - 4}$

Step 1

Rewrite the equation as $\frac{a}{a - 4} = 8$ .

$\frac{a}{a - 4} = 8$

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.

$a - 4, 1$

Step 2.2

Remove parentheses.

$a - 4, 1$

Step 2.3

The LCM of one and any expression is the expression.

$a - 4$

Step 3

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

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Step 3.1

Multiply each term in $\frac{a}{a - 4} = 8$ by $a - 4$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $a - 4$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

$a = 8 (a - 4)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$a = 8 a + 8 \cdot - 4$

Step 3.3.2

Multiply $8$ by $- 4$ .

$a = 8 a - 32$

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 $8 a$ from both sides of the equation.

$a - 8 a = - 32$

Step 4.1.2

Subtract $8 a$ from $a$ .

$- 7 a = - 32$

Step 4.2

Divide each term in $- 7 a = - 32$ by $- 7$ and simplify.

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Step 4.2.1

Divide each term in $- 7 a = - 32$ by $- 7$ .

$\frac{- 7 a}{- 7} = \frac{- 32}{- 7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 7 a}{- 7} = \frac{- 32}{- 7}$

Step 4.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 32}{- 7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Dividing two negative values results in a positive value.

$a = \frac{32}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \frac{32}{7}$

Decimal Form:

$a = 4.\overline{571428}$

Mixed Number Form:

$a = 4 \frac{4}{7}$