Basic Math Examples

$k y^{2} + (k + 1) y + k - 1 = 0$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$k y^{2} + k y + 1 y + k - 1 = 0$

Step 1.2

Multiply $y$ by $1$ .

$k y^{2} + k y + y + k - 1 = 0$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $y$ from both sides of the equation.

$k y^{2} + k y + k - 1 = - y$

Step 2.2

Add $1$ to both sides of the equation.

$k y^{2} + k y + k = - y + 1$

Step 3

Factor $k$ out of $k y^{2} + k y + k$ .

Tap for more steps...

Step 3.1

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

$k (y^{2}) + k y + k = - y + 1$

Step 3.2

Factor $k$ out of $k y$ .

$k (y^{2}) + k (y) + k = - y + 1$

Step 3.3

Raise $k$ to the power of $1$ .

$k (y^{2}) + k (y) + k = - y + 1$

Step 3.4

Factor $k$ out of $k^{1}$ .

$k (y^{2}) + k (y) + k \cdot 1 = - y + 1$

Step 3.5

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

$k (y^{2} + y) + k \cdot 1 = - y + 1$

Step 3.6

Factor $k$ out of $k (y^{2} + y) + k \cdot 1$ .

$k (y^{2} + y + 1) = - y + 1$

Step 4

Divide each term in $k (y^{2} + y + 1) = - y + 1$ by $y^{2} + y + 1$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $k (y^{2} + y + 1) = - y + 1$ by $y^{2} + y + 1$ .

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

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $y^{2} + y + 1$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $k$ by $1$ .

$k = \frac{- y}{y^{2} + y + 1} + \frac{1}{y^{2} + y + 1}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Combine the numerators over the common denominator.

$k = \frac{- y + 1}{y^{2} + y + 1}$

Step 4.3.2

Factor $- 1$ out of $- y$ .

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

Step 4.3.3

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 4.3.4

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

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

Step 4.3.5

Simplify the expression.

Tap for more steps...

Step 4.3.5.1

Rewrite $- (y - 1)$ as $- 1 (y - 1)$ .

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

Step 4.3.5.2

Move the negative in front of the fraction.

$k = - \frac{y - 1}{y^{2} + y + 1}$