Basic Math Examples

$\frac{y - 8}{y - 3} = \frac{y - 9}{y + 9}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$(y - 8) (y + 9) = (y - 3) (y - 9)$

Step 2

Solve the equation for $y$ .

Tap for more steps...

Step 2.1

Simplify $(y - 8) (y + 9)$ .

Tap for more steps...

Step 2.1.1

Rewrite.

$0 + 0 + (y - 8) (y + 9) = (y - 3) (y - 9)$

Step 2.1.2

Simplify by adding zeros.

$(y - 8) (y + 9) = (y - 3) (y - 9)$

Step 2.1.3

Expand $(y - 8) (y + 9)$ using the FOIL Method.

Tap for more steps...

Step 2.1.3.1

Apply the distributive property.

$y (y + 9) - 8 (y + 9) = (y - 3) (y - 9)$

Step 2.1.3.2

Apply the distributive property.

$y \cdot y + y \cdot 9 - 8 (y + 9) = (y - 3) (y - 9)$

Step 2.1.3.3

Apply the distributive property.

$y \cdot y + y \cdot 9 - 8 y - 8 \cdot 9 = (y - 3) (y - 9)$

Step 2.1.4

Simplify and combine like terms.

Tap for more steps...

Step 2.1.4.1

Simplify each term.

Tap for more steps...

Step 2.1.4.1.1

Multiply $y$ by $y$ .

$y^{2} + y \cdot 9 - 8 y - 8 \cdot 9 = (y - 3) (y - 9)$

Step 2.1.4.1.2

Move $9$ to the left of $y$ .

$y^{2} + 9 \cdot y - 8 y - 8 \cdot 9 = (y - 3) (y - 9)$

Step 2.1.4.1.3

Multiply $- 8$ by $9$ .

$y^{2} + 9 y - 8 y - 72 = (y - 3) (y - 9)$

Step 2.1.4.2

Subtract $8 y$ from $9 y$ .

$y^{2} + y - 72 = (y - 3) (y - 9)$

Step 2.2

Simplify $(y - 3) (y - 9)$ .

Tap for more steps...

Step 2.2.1

Expand $(y - 3) (y - 9)$ using the FOIL Method.

Tap for more steps...

Step 2.2.1.1

Apply the distributive property.

$y^{2} + y - 72 = y (y - 9) - 3 (y - 9)$

Step 2.2.1.2

Apply the distributive property.

$y^{2} + y - 72 = y \cdot y + y \cdot - 9 - 3 (y - 9)$

Step 2.2.1.3

Apply the distributive property.

$y^{2} + y - 72 = y \cdot y + y \cdot - 9 - 3 y - 3 \cdot - 9$

Step 2.2.2

Simplify and combine like terms.

Tap for more steps...

Step 2.2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.2.1.1

Multiply $y$ by $y$ .

$y^{2} + y - 72 = y^{2} + y \cdot - 9 - 3 y - 3 \cdot - 9$

Step 2.2.2.1.2

Move $- 9$ to the left of $y$ .

$y^{2} + y - 72 = y^{2} - 9 \cdot y - 3 y - 3 \cdot - 9$

Step 2.2.2.1.3

Multiply $- 3$ by $- 9$ .

$y^{2} + y - 72 = y^{2} - 9 y - 3 y + 27$

Step 2.2.2.2

Subtract $3 y$ from $- 9 y$ .

$y^{2} + y - 72 = y^{2} - 12 y + 27$

Step 2.3

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

Tap for more steps...

Step 2.3.1

Subtract $y^{2}$ from both sides of the equation.

$y^{2} + y - 72 - y^{2} = - 12 y + 27$

Step 2.3.2

Add $12 y$ to both sides of the equation.

$y^{2} + y - 72 - y^{2} + 12 y = 27$

Step 2.3.3

Combine the opposite terms in $y^{2} + y - 72 - y^{2} + 12 y$ .

Tap for more steps...

Step 2.3.3.1

Subtract $y^{2}$ from $y^{2}$ .

$y - 72 + 0 + 12 y = 27$

Step 2.3.3.2

Add $y - 72$ and $0$ .

$y - 72 + 12 y = 27$

Step 2.3.4

Add $y$ and $12 y$ .

$13 y - 72 = 27$

Step 2.4

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

Tap for more steps...

Step 2.4.1

Add $72$ to both sides of the equation.

$13 y = 27 + 72$

Step 2.4.2

Add $27$ and $72$ .

$13 y = 99$

Step 2.5

Divide each term in $13 y = 99$ by $13$ and simplify.

Tap for more steps...

Step 2.5.1

Divide each term in $13 y = 99$ by $13$ .

$\frac{13 y}{13} = \frac{99}{13}$

Step 2.5.2

Simplify the left side.

Tap for more steps...

Step 2.5.2.1

Cancel the common factor of $13$ .

Tap for more steps...

Step 2.5.2.1.1

Cancel the common factor.

$\frac{13 y}{13} = \frac{99}{13}$

Step 2.5.2.1.2

Divide $y$ by $1$ .

$y = \frac{99}{13}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{99}{13}$

Decimal Form:

$y = 7.\overline{615384}$

Mixed Number Form:

$y = 7 \frac{8}{13}$