Calculus Examples

$y \frac{1}{2} - 6 y \frac{1}{4} + 8 = 0$

Step 1

Simplify $y (\frac{1}{2}) - 6 y \frac{1}{4} + 8$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $y$ and $\frac{1}{2}$ .

$\frac{y}{2} - 6 y \frac{1}{4} + 8 = 0$

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Factor $2$ out of $- 6 y$ .

$\frac{y}{2} + 2 (- 3 y) \frac{1}{4} + 8 = 0$

Step 1.1.2.2

Factor $2$ out of $4$ .

$\frac{y}{2} + 2 (- 3 y) \frac{1}{2 (2)} + 8 = 0$

Step 1.1.2.3

Cancel the common factor.

$\frac{y}{2} + 2 (- 3 y) \frac{1}{2 \cdot 2} + 8 = 0$

Step 1.1.2.4

Rewrite the expression.

$\frac{y}{2} - 3 y \frac{1}{2} + 8 = 0$

Step 1.1.3

Combine $- 3$ and $\frac{1}{2}$ .

$\frac{y}{2} + y \frac{- 3}{2} + 8 = 0$

Step 1.1.4

Combine $y$ and $\frac{- 3}{2}$ .

$\frac{y}{2} + \frac{y \cdot - 3}{2} + 8 = 0$

Step 1.1.5

Move $- 3$ to the left of $y$ .

$\frac{y}{2} + \frac{- 3 \cdot y}{2} + 8 = 0$

Step 1.1.6

Move the negative in front of the fraction.

$\frac{y}{2} - \frac{3 y}{2} + 8 = 0$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$8 + \frac{y - 3 y}{2} = 0$

Step 1.2.2

Subtract $3 y$ from $y$ .

$8 + \frac{- 2 y}{2} = 0$

Step 1.2.3

Cancel the common factor of $- 2$ and $2$ .

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Step 1.2.3.1

Factor $2$ out of $- 2 y$ .

$8 + \frac{2 (- y)}{2} = 0$

Step 1.2.3.2

Cancel the common factors.

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Step 1.2.3.2.1

Factor $2$ out of $2$ .

$8 + \frac{2 (- y)}{2 (1)} = 0$

Step 1.2.3.2.2

Cancel the common factor.

$8 + \frac{2 (- y)}{2 \cdot 1} = 0$

Step 1.2.3.2.3

Rewrite the expression.

$8 + \frac{- y}{1} = 0$

Step 1.2.3.2.4

Divide $- y$ by $1$ .

$8 - y = 0$

Step 2

Subtract $8$ from both sides of the equation.

$- y = - 8$

Step 3

Divide each term in $- y = - 8$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = - 8$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 8}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 8}{- 1}$

Step 3.2.2

Divide $y$ by $1$ .

$y = \frac{- 8}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 8$ by $- 1$ .

$y = 8$