Algebra Examples

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

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Reduce the expression $\frac{2 a}{a}$ by cancelling the common factors.

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Step 1.1.1

Cancel the common factor.

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

Step 1.1.2

Rewrite the expression.

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

Step 1.2

Divide $2$ by $1$ .

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

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.

$1, a, 1$

Step 2.2

The LCM of one and any expression is the expression.

$a$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $a$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

$2 a + 1 = 4 a$

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 $4 a$ from both sides of the equation.

$2 a + 1 - 4 a = 0$

Step 4.1.2

Subtract $4 a$ from $2 a$ .

$- 2 a + 1 = 0$

Step 4.2

Subtract $1$ from both sides of the equation.

$- 2 a = - 1$

Step 4.3

Divide each term in $- 2 a = - 1$ by $- 2$ and simplify.

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Step 4.3.1

Divide each term in $- 2 a = - 1$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{- 1}{- 2}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 2$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{- 1}{- 2}$

Step 4.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 1}{- 2}$

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.

$a = \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1}{2}$

Decimal Form:

$a = 0.5$