Finite Math Examples

$x^{2} + (1 - a) x - a = 0$

Step 1

Simplify.

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $x$ by $1$ .

$x^{2} + x - y x - y = 0$

Step 1.2

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

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Step 1.2.1

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

$x - y x - y = - x^{2}$

Step 1.2.2

Subtract $x$ from both sides of the equation.

$- y x - y = - x^{2} - x$

Step 1.3

Factor $y$ out of $- y x - y$ .

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Step 1.3.1

Factor $y$ out of $- y x$ .

$y (- 1 x) - y = - x^{2} - x$

Step 1.3.2

Factor $y$ out of $- y$ .

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

Step 1.3.3

Factor $y$ out of $y (- 1 x) + y \cdot - 1$ .

$y (- 1 x - 1) = - x^{2} - x$

Step 1.4

Rewrite $- 1 x$ as $- x$ .

$y (- x - 1) = - x^{2} - x$

Step 1.5

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

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Step 1.5.1

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

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

Step 1.5.2

Simplify the left side.

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Step 1.5.2.1

Cancel the common factor of $- x - 1$ .

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Step 1.5.2.1.1

Cancel the common factor.

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

Step 1.5.2.1.2

Divide $y$ by $1$ .

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

Step 1.5.3

Simplify the right side.

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Step 1.5.3.1

Combine the numerators over the common denominator.

$y = \frac{- x^{2} - x}{- x - 1}$

Step 1.5.3.2

Factor $x$ out of $- x^{2} - x$ .

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Step 1.5.3.2.1

Factor $x$ out of $- x^{2}$ .

$y = \frac{x (- x) - x}{- x - 1}$

Step 1.5.3.2.2

Factor $x$ out of $- x$ .

$y = \frac{x (- x) + x \cdot - 1}{- x - 1}$

Step 1.5.3.2.3

Factor $x$ out of $x (- x) + x \cdot - 1$ .

$y = \frac{x (- x - 1)}{- x - 1}$

Step 1.5.3.3

Cancel the common factor of $- x - 1$ .

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Step 1.5.3.3.1

Cancel the common factor.

$y = \frac{x (- x - 1)}{- x - 1}$

Step 1.5.3.3.2

Divide $x$ by $1$ .

$y = x$

Step 2

Since $y = x$ is not a rational expression, there are no asymptotes.

No Asymptotes

Step 3