Basic Math Examples

$\frac{9 y - 3}{- 2 y + 4} = 2$

Step 1

Factor each term.

Tap for more steps...

Step 1.1

Factor $3$ out of $9 y - 3$ .

Tap for more steps...

Step 1.1.1

Factor $3$ out of $9 y$ .

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

Step 1.1.2

Factor $3$ out of $- 3$ .

$\frac{3 (3 y) + 3 (- 1)}{- 2 y + 4} = 2$

Step 1.1.3

Factor $3$ out of $3 (3 y) + 3 (- 1)$ .

$\frac{3 (3 y - 1)}{- 2 y + 4} = 2$

Step 1.2

Factor $2$ out of $- 2 y + 4$ .

Tap for more steps...

Step 1.2.1

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

$\frac{3 (3 y - 1)}{2 (- y) + 4} = 2$

Step 1.2.2

Factor $2$ out of $4$ .

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

Step 1.2.3

Factor $2$ out of $2 (- y) + 2 (2)$ .

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

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

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

$2 (- y + 2), 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 (- y + 2)$

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Rewrite using the commutative property of multiplication.

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

Step 3.2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.2.1

Cancel the common factor.

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

Step 3.2.2.2

Rewrite the expression.

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

Step 3.2.3

Multiply $\frac{3 (3 y - 1)}{- y + 2}$ by $- y + 2$ .

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

Step 3.2.4

Cancel the common factor of $- y + 2$ .

Tap for more steps...

Step 3.2.4.1

Cancel the common factor.

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

Step 3.2.4.2

Divide $3 (3 y - 1)$ by $1$ .

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

Step 3.2.5

Apply the distributive property.

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

Step 3.2.6

Multiply.

Tap for more steps...

Step 3.2.6.1

Multiply $3$ by $3$ .

$9 y + 3 \cdot - 1 = 2 (2 (- y + 2))$

Step 3.2.6.2

Multiply $3$ by $- 1$ .

$9 y - 3 = 2 (2 (- y + 2))$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Apply the distributive property.

$9 y - 3 = 2 (2 (- y) + 2 \cdot 2)$

Step 3.3.2

Multiply.

Tap for more steps...

Step 3.3.2.1

Multiply $- 1$ by $2$ .

$9 y - 3 = 2 (- 2 y + 2 \cdot 2)$

Step 3.3.2.2

Multiply $2$ by $2$ .

$9 y - 3 = 2 (- 2 y + 4)$

Step 3.3.3

Apply the distributive property.

$9 y - 3 = 2 (- 2 y) + 2 \cdot 4$

Step 3.3.4

Multiply.

Tap for more steps...

Step 3.3.4.1

Multiply $- 2$ by $2$ .

$9 y - 3 = - 4 y + 2 \cdot 4$

Step 3.3.4.2

Multiply $2$ by $4$ .

$9 y - 3 = - 4 y + 8$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Add $4 y$ to both sides of the equation.

$9 y - 3 + 4 y = 8$

Step 4.1.2

Add $9 y$ and $4 y$ .

$13 y - 3 = 8$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Add $3$ to both sides of the equation.

$13 y = 8 + 3$

Step 4.2.2

Add $8$ and $3$ .

$13 y = 11$

Step 4.3

Divide each term in $13 y = 11$ by $13$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $13 y = 11$ by $13$ .

$\frac{13 y}{13} = \frac{11}{13}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $13$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{13 y}{13} = \frac{11}{13}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{11}{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{11}{13}$

Decimal Form:

$y = 0.\overline{846153}$