Algebra Examples

$\frac{y^{2} + 7 y - 18}{C} \cdot \frac{14 y^{2}}{7 y^{2} - 14 y} = 1$

Step 1

Simplify $\frac{y^{2} + 7 y - 18}{C} \cdot \frac{14 y^{2}}{7 y^{2} - 14 y}$ .

Tap for more steps...

Step 1.1

Factor $y^{2} + 7 y - 18$ using the AC method.

Tap for more steps...

Step 1.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 18$ and whose sum is $7$ .

$- 2, 9$

Step 1.1.2

Write the factored form using these integers.

$\frac{(y - 2) (y + 9)}{C} \cdot \frac{14 y^{2}}{7 y^{2} - 14 y} = 1$

Step 1.2

Simplify terms.

Tap for more steps...

Step 1.2.1

Factor $7 y$ out of $7 y^{2} - 14 y$ .

Tap for more steps...

Step 1.2.1.1

Factor $7 y$ out of $7 y^{2}$ .

$\frac{(y - 2) (y + 9)}{C} \cdot \frac{14 y^{2}}{7 y (y) - 14 y} = 1$

Step 1.2.1.2

Factor $7 y$ out of $- 14 y$ .

$\frac{(y - 2) (y + 9)}{C} \cdot \frac{14 y^{2}}{7 y (y) + 7 y (- 2)} = 1$

Step 1.2.1.3

Factor $7 y$ out of $7 y (y) + 7 y (- 2)$ .

$\frac{(y - 2) (y + 9)}{C} \cdot \frac{14 y^{2}}{7 y (y - 2)} = 1$

Step 1.2.2

Combine.

$\frac{(y - 2) (y + 9) (14 y^{2})}{C (7 y (y - 2))} = 1$

Step 1.2.3

Cancel the common factor of $y - 2$ .

Tap for more steps...

Step 1.2.3.1

Cancel the common factor.

$\frac{(y - 2) (y + 9) (14 y^{2})}{C (7 y (y - 2))} = 1$

Step 1.2.3.2

Rewrite the expression.

$\frac{(y + 9) (14 y^{2})}{C (7 y)} = 1$

Step 1.2.4

Cancel the common factor of $14$ and $7$ .

Tap for more steps...

Step 1.2.4.1

Factor $7$ out of $(y + 9) (14 y^{2})$ .

$\frac{7 ((y + 9) (2 y^{2}))}{C (7 y)} = 1$

Step 1.2.4.2

Cancel the common factors.

Tap for more steps...

Step 1.2.4.2.1

Factor $7$ out of $C (7 y)$ .

$\frac{7 ((y + 9) (2 y^{2}))}{7 (C (y))} = 1$

Step 1.2.4.2.2

Cancel the common factor.

$\frac{7 ((y + 9) (2 y^{2}))}{7 (C (y))} = 1$

Step 1.2.4.2.3

Rewrite the expression.

$\frac{(y + 9) (2 y^{2})}{C (y)} = 1$

Step 1.2.5

Cancel the common factor of $y^{2}$ and $y$ .

Tap for more steps...

Step 1.2.5.1

Factor $y$ out of $(y + 9) (2 y^{2})$ .

$\frac{y ((y + 9) (2 y))}{C (y)} = 1$

Step 1.2.5.2

Cancel the common factors.

Tap for more steps...

Step 1.2.5.2.1

Factor $y$ out of $C (y)$ .

$\frac{y ((y + 9) (2 y))}{y C} = 1$

Step 1.2.5.2.2

Cancel the common factor.

$\frac{y ((y + 9) (2 y))}{y C} = 1$

Step 1.2.5.2.3

Rewrite the expression.

$\frac{(y + 9) (2 y)}{C} = 1$

Step 1.2.6

Simplify the expression.

Tap for more steps...

Step 1.2.6.1

Move $2$ to the left of $y + 9$ .

$\frac{2 \cdot (y + 9) y}{C} = 1$

Step 1.2.6.2

Reorder factors in $\frac{2 (y + 9) y}{C}$ .

$\frac{2 y (y + 9)}{C} = 1$

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.

$C, 1$

Step 2.2

The LCM of one and any expression is the expression.

$C$

Step 3

Multiply each term in $\frac{2 y (y + 9)}{C} = 1$ by $C$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $\frac{2 y (y + 9)}{C} = 1$ by $C$ .

$\frac{2 y (y + 9)}{C} C = 1 C$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $C$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{2 y (y + 9)}{C} C = 1 C$

Step 3.2.1.2

Rewrite the expression.

$2 y (y + 9) = 1 C$

Step 3.2.2

Apply the distributive property.

$2 y \cdot y + 2 y \cdot 9 = 1 C$

Step 3.2.3

Multiply $y$ by $y$ by adding the exponents.

Tap for more steps...

Step 3.2.3.1

Move $y$ .

$2 (y \cdot y) + 2 y \cdot 9 = 1 C$

Step 3.2.3.2

Multiply $y$ by $y$ .

$2 y^{2} + 2 y \cdot 9 = 1 C$

Step 3.2.4

Multiply $9$ by $2$ .

$2 y^{2} + 18 y = 1 C$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Multiply $C$ by $1$ .

$2 y^{2} + 18 y = C$

Step 4

Rewrite the equation as $C = 2 y^{2} + 18 y$ .

$C = 2 y^{2} + 18 y$