Algebra Examples

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

Step 1

Find the LCD of the terms in the equation.

Tap for more steps...

Step 1.1

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 1.2

The LCM of one and any expression is the expression.

$x$

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $x$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

$x + 1 = 3 y x + 1 x$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Multiply $x$ by $1$ .

$x + 1 = 3 y x + x$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 y x + x = x + 1$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Subtract $x$ from both sides of the equation.

$3 y x + x - x = 1$

Step 3.2.2

Combine the opposite terms in $3 y x + x - x$ .

Tap for more steps...

Step 3.2.2.1

Subtract $x$ from $x$ .

$3 y x + 0 = 1$

Step 3.2.2.2

Add $3 y x$ and $0$ .

$3 y x = 1$

Step 3.3

Divide each term in $3 y x = 1$ by $3 y$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $3 y x = 1$ by $3 y$ .

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

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

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

Step 3.3.2.1.2

Rewrite the expression.

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

Step 3.3.2.2

Cancel the common factor of $y$ .

Tap for more steps...

Step 3.3.2.2.1

Cancel the common factor.

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

Step 3.3.2.2.2

Divide $x$ by $1$ .

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