Precalculus Examples

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

Step 1

Rewrite the equation as $\frac{1}{x} + 1 = y$ .

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

Step 2

Subtract $1$ from both sides of the equation.

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

Step 3

Find the LCD of the terms in the equation.

Tap for more steps...

Step 3.1

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

$x, 1, 1$

Step 3.2

The LCM of one and any expression is the expression.

$x$

Step 4

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

Tap for more steps...

Step 4.1

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

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

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Rewrite the expression.

$1 = y x - x$

Step 5

Solve the equation.

Tap for more steps...

Step 5.1

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

$y x - x = 1$

Step 5.2

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

Tap for more steps...

Step 5.2.1

Factor $x$ out of $y x$ .

$x y - x = 1$

Step 5.2.2

Factor $x$ out of $- x$ .

$x y + x \cdot - 1 = 1$

Step 5.2.3

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

$x (y - 1) = 1$

Step 5.3

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

Tap for more steps...

Step 5.3.1

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

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

Step 5.3.2

Simplify the left side.

Tap for more steps...

Step 5.3.2.1

Cancel the common factor of $y - 1$ .

Tap for more steps...

Step 5.3.2.1.1

Cancel the common factor.

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

Step 5.3.2.1.2

Divide $x$ by $1$ .

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