Basic Math Examples

$\frac{y + 5}{y - 3} + 4 = 2$

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.

$y - 3, 1, 1$

Step 1.2

Remove parentheses.

$y - 3, 1, 1$

Step 1.3

The LCM of one and any expression is the expression.

$y - 3$

Step 2

Multiply each term in $\frac{y + 5}{y - 3} + 4 = 2$ by $y - 3$ to eliminate the fractions.

Tap for more steps...

Step 2.1

Multiply each term in $\frac{y + 5}{y - 3} + 4 = 2$ by $y - 3$ .

$\frac{y + 5}{y - 3} (y - 3) + 4 (y - 3) = 2 (y - 3)$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1

Cancel the common factor of $y - 3$ .

Tap for more steps...

Step 2.2.1.1.1

Cancel the common factor.

$\frac{y + 5}{y - 3} (y - 3) + 4 (y - 3) = 2 (y - 3)$

Step 2.2.1.1.2

Rewrite the expression.

$y + 5 + 4 (y - 3) = 2 (y - 3)$

Step 2.2.1.2

Apply the distributive property.

$y + 5 + 4 y + 4 \cdot - 3 = 2 (y - 3)$

Step 2.2.1.3

Multiply $4$ by $- 3$ .

$y + 5 + 4 y - 12 = 2 (y - 3)$

Step 2.2.2

Simplify by adding terms.

Tap for more steps...

Step 2.2.2.1

Add $y$ and $4 y$ .

$5 y + 5 - 12 = 2 (y - 3)$

Step 2.2.2.2

Subtract $12$ from $5$ .

$5 y - 7 = 2 (y - 3)$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Apply the distributive property.

$5 y - 7 = 2 y + 2 \cdot - 3$

Step 2.3.2

Multiply $2$ by $- 3$ .

$5 y - 7 = 2 y - 6$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

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

$5 y - 7 - 2 y = - 6$

Step 3.1.2

Subtract $2 y$ from $5 y$ .

$3 y - 7 = - 6$

Step 3.2

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 3.2.1

Add $7$ to both sides of the equation.

$3 y = - 6 + 7$

Step 3.2.2

Add $- 6$ and $7$ .

$3 y = 1$

Step 3.3

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

Tap for more steps...

Step 3.3.1

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

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

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.

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

Step 3.3.2.1.2

Divide $y$ by $1$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 0.\overline{3}$