Basic Math Examples

$2 y = y + \frac{F}{y}$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

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

$1, 1, y$

Step 1.2

The LCM of one and any expression is the expression.

$y$

Step 2

Multiply each term in $2 y = y + \frac{F}{y}$ by $y$ to eliminate the fractions.

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Step 2.1

Multiply each term in $2 y = y + \frac{F}{y}$ by $y$ .

$2 y \cdot y = y \cdot y + \frac{F}{y} y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $y$ by $y$ by adding the exponents.

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Step 2.2.1.1

Move $y$ .

$2 (y \cdot y) = y \cdot y + \frac{F}{y} y$

Step 2.2.1.2

Multiply $y$ by $y$ .

$2 y^{2} = y \cdot y + \frac{F}{y} y$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $y$ by $y$ .

$2 y^{2} = y^{2} + \frac{F}{y} y$

Step 2.3.1.2

Cancel the common factor of $y$ .

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Step 2.3.1.2.1

Cancel the common factor.

$2 y^{2} = y^{2} + \frac{F}{y} y$

Step 2.3.1.2.2

Rewrite the expression.

$2 y^{2} = y^{2} + F$

Step 3

Solve the equation.

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Step 3.1

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

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Step 3.1.1

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

$2 y^{2} - y^{2} = F$

Step 3.1.2

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

$y^{2} = F$

Step 3.2

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

$y = \pm \sqrt{F}$

Step 3.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.3.1

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{F}$

Step 3.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{F}$

Step 3.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{F}$

$y = - \sqrt{F}$

$y = \sqrt{F}$

$y = - \sqrt{F}$

$y = \sqrt{F}$

$y = - \sqrt{F}$