Pre-Algebra Examples

$2 x + \frac{1}{y} = 3$

Step 1

Subtract $2 x$ from both sides of the equation.

$\frac{1}{y} = 3 - 2 x$

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.

$y, 1, 1$

Step 2.2

The LCM of one and any expression is the expression.

$y$

Step 3

Multiply each term in $\frac{1}{y} = 3 - 2 x$ by $y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{1}{y} = 3 - 2 x$ by $y$ .

$\frac{1}{y} y = 3 y - 2 x y$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $y$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{1}{y} y = 3 y - 2 x y$

Step 3.2.1.2

Rewrite the expression.

$1 = 3 y - 2 x y$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $3 y - 2 x y = 1$ .

$3 y - 2 x y = 1$

Step 4.2

Factor $y$ out of $3 y - 2 x y$ .

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Step 4.2.1

Factor $y$ out of $3 y$ .

$y \cdot 3 - 2 x y = 1$

Step 4.2.2

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

$y \cdot 3 + y (- 2 x) = 1$

Step 4.2.3

Factor $y$ out of $y \cdot 3 + y (- 2 x)$ .

$y (3 - 2 x) = 1$

Step 4.3

Divide each term in $y (3 - 2 x) = 1$ by $3 - 2 x$ and simplify.

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Step 4.3.1

Divide each term in $y (3 - 2 x) = 1$ by $3 - 2 x$ .

$\frac{y (3 - 2 x)}{3 - 2 x} = \frac{1}{3 - 2 x}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $3 - 2 x$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{y (3 - 2 x)}{3 - 2 x} = \frac{1}{3 - 2 x}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{3 - 2 x}$