Precalculus Examples

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

Step 1

Multiply the equation by $y - 2$ .

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

Step 2

Simplify the left side.

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Step 2.1

Apply the distributive property.

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

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $y - 2$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

$y x - 2 x = y + 3$

Step 4

Solve for $y$ .

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Step 4.1

Subtract $y$ from both sides of the equation.

$y x - 2 x - y = 3$

Step 4.2

Add $2 x$ to both sides of the equation.

$y x - y = 3 + 2 x$

Step 4.3

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

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Step 4.3.1

Factor $y$ out of $y x$ .

$y (x) - y = 3 + 2 x$

Step 4.3.2

Factor $y$ out of $- y$ .

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

Step 4.3.3

Factor $y$ out of $y (x) + y \cdot - 1$ .

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

Step 4.4

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

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Step 4.4.1

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

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

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $x - 1$ .

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Step 4.4.2.1.1

Cancel the common factor.

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

Step 4.4.2.1.2

Divide $y$ by $1$ .

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

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Combine the numerators over the common denominator.

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