Basic Math Examples

$1 - (a - \frac{4}{a}) = 1 - 4 a^{- 2} (1 - a)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$1 - a - - \frac{4}{a} = 1 - 4 a^{- 2} (1 - a)$

Step 1.2

Multiply $- - \frac{4}{a}$ .

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Step 1.2.1

Multiply $- 1$ by $- 1$ .

$1 - a + 1 \frac{4}{a} = 1 - 4 a^{- 2} (1 - a)$

Step 1.2.2

Multiply $\frac{4}{a}$ by $1$ .

$1 - a + \frac{4}{a} = 1 - 4 a^{- 2} (1 - a)$

Step 2

Simplify each term.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$1 - a + \frac{4}{a} = 1 - 4 \frac{1}{a^{2}} (1 - a)$

Step 2.2

Combine $- 4$ and $\frac{1}{a^{2}}$ .

$1 - a + \frac{4}{a} = 1 + \frac{- 4}{a^{2}} (1 - a)$

Step 2.3

Move the negative in front of the fraction.

$1 - a + \frac{4}{a} = 1 - \frac{4}{a^{2}} (1 - a)$

Step 2.4

Apply the distributive property.

$1 - a + \frac{4}{a} = 1 - \frac{4}{a^{2}} \cdot 1 - \frac{4}{a^{2}} (- a)$

Step 2.5

Multiply $- 1$ by $1$ .

$1 - a + \frac{4}{a} = 1 - \frac{4}{a^{2}} - \frac{4}{a^{2}} (- a)$

Step 2.6

Cancel the common factor of $a$ .

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Step 2.6.1

Move the leading negative in $- \frac{4}{a^{2}}$ into the numerator.

$1 - a + \frac{4}{a} = 1 - \frac{4}{a^{2}} + \frac{- 4}{a^{2}} (- a)$

Step 2.6.2

Factor $a$ out of $a^{2}$ .

$1 - a + \frac{4}{a} = 1 - \frac{4}{a^{2}} + \frac{- 4}{a \cdot a} (- a)$

Step 2.6.3

Factor $a$ out of $- a$ .

$1 - a + \frac{4}{a} = 1 - \frac{4}{a^{2}} + \frac{- 4}{a \cdot a} (a \cdot - 1)$

Step 2.6.4

Cancel the common factor.

$1 - a + \frac{4}{a} = 1 - \frac{4}{a^{2}} + \frac{- 4}{a \cdot a} (a \cdot - 1)$

Step 2.6.5

Rewrite the expression.

$1 - a + \frac{4}{a} = 1 - \frac{4}{a^{2}} + \frac{- 4}{a} \cdot - 1$

Step 2.7

Combine $\frac{- 4}{a}$ and $- 1$ .

$1 - a + \frac{4}{a} = 1 - \frac{4}{a^{2}} + \frac{- 4 \cdot - 1}{a}$

Step 2.8

Multiply $- 4$ by $- 1$ .

$1 - a + \frac{4}{a} = 1 - \frac{4}{a^{2}} + \frac{4}{a}$

Step 3

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

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Step 3.1

Add $\frac{4}{a^{2}}$ to both sides of the equation.

$1 - a + \frac{4}{a} + \frac{4}{a^{2}} = 1 + \frac{4}{a}$

Step 3.2

Subtract $\frac{4}{a}$ from both sides of the equation.

$1 - a + \frac{4}{a} + \frac{4}{a^{2}} - \frac{4}{a} = 1$

Step 3.3

Combine the opposite terms in $1 - a + \frac{4}{a} + \frac{4}{a^{2}} - \frac{4}{a}$ .

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Step 3.3.1

Subtract $\frac{4}{a}$ from $\frac{4}{a}$ .

$1 - a + \frac{4}{a^{2}} + 0 = 1$

Step 3.3.2

Add $1 - a + \frac{4}{a^{2}}$ and $0$ .

$1 - a + \frac{4}{a^{2}} = 1$

Step 4

Find the LCD of the terms in the equation.

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Step 4.1

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

$1, 1, a^{2}, 1$

Step 4.2

The LCM of one and any expression is the expression.

$a^{2}$

Step 5

Multiply each term in $1 - a + \frac{4}{a^{2}} = 1$ by $a^{2}$ to eliminate the fractions.

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Step 5.1

Multiply each term in $1 - a + \frac{4}{a^{2}} = 1$ by $a^{2}$ .

$1 a^{2} - a \cdot a^{2} + \frac{4}{a^{2}} a^{2} = 1 a^{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Multiply $a^{2}$ by $1$ .

$a^{2} - a \cdot a^{2} + \frac{4}{a^{2}} a^{2} = 1 a^{2}$

Step 5.2.1.2

Multiply $a$ by $a^{2}$ by adding the exponents.

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Step 5.2.1.2.1

Move $a^{2}$ .

$a^{2} - (a^{2} a) + \frac{4}{a^{2}} a^{2} = 1 a^{2}$

Step 5.2.1.2.2

Multiply $a^{2}$ by $a$ .

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Step 5.2.1.2.2.1

Raise $a$ to the power of $1$ .

$a^{2} - (a^{2} a^{1}) + \frac{4}{a^{2}} a^{2} = 1 a^{2}$

Step 5.2.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a^{2} - a^{2 + 1} + \frac{4}{a^{2}} a^{2} = 1 a^{2}$

Step 5.2.1.2.3

Add $2$ and $1$ .

$a^{2} - a^{3} + \frac{4}{a^{2}} a^{2} = 1 a^{2}$

Step 5.2.1.3

Cancel the common factor of $a^{2}$ .

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Step 5.2.1.3.1

Cancel the common factor.

$a^{2} - a^{3} + \frac{4}{a^{2}} a^{2} = 1 a^{2}$

Step 5.2.1.3.2

Rewrite the expression.

$a^{2} - a^{3} + 4 = 1 a^{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply $a^{2}$ by $1$ .

$a^{2} - a^{3} + 4 = a^{2}$

Step 6

Solve the equation.

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Step 6.1

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

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Step 6.1.1

Subtract $a^{2}$ from both sides of the equation.

$a^{2} - a^{3} + 4 - a^{2} = 0$

Step 6.1.2

Combine the opposite terms in $a^{2} - a^{3} + 4 - a^{2}$ .

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Step 6.1.2.1

Subtract $a^{2}$ from $a^{2}$ .

$- a^{3} + 4 + 0 = 0$

Step 6.1.2.2

Add $- a^{3} + 4$ and $0$ .

$- a^{3} + 4 = 0$

Step 6.2

Subtract $4$ from both sides of the equation.

$- a^{3} = - 4$

Step 6.3

Divide each term in $- a^{3} = - 4$ by $- 1$ and simplify.

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Step 6.3.1

Divide each term in $- a^{3} = - 4$ by $- 1$ .

$\frac{- a^{3}}{- 1} = \frac{- 4}{- 1}$

Step 6.3.2

Simplify the left side.

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Step 6.3.2.1

Dividing two negative values results in a positive value.

$\frac{a^{3}}{1} = \frac{- 4}{- 1}$

Step 6.3.2.2

Divide $a^{3}$ by $1$ .

$a^{3} = \frac{- 4}{- 1}$

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Divide $- 4$ by $- 1$ .

$a^{3} = 4$

Step 6.4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$a = \sqrt[3]{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = \sqrt[3]{4}$

Decimal Form:

$a = 1.58740105 \dots$