Precalculus Examples

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

Step 1

Simplify $\frac{x^{2 - 1}}{x^{2 - 2 x + 1}}$ .

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Step 1.1

Cancel the common factor of $x^{2 - 1}$ and $x^{2 - 2 x + 1}$ .

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Step 1.1.1

Factor $x^{2 - 2 x + 1}$ out of $x^{2 - 1}$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Multiply by $1$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.1.2.4

Divide $x^{1 - (2 - 2 x + 1)}$ by $1$ .

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

Step 1.2

Simplify each term.

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Step 1.2.1

Add $2$ and $1$ .

$y = x^{1 - (- 2 x + 3)}$

Step 1.2.2

Apply the distributive property.

$y = x^{1 - (- 2 x) - 1 \cdot 3}$

Step 1.2.3

Multiply $- 2$ by $- 1$ .

$y = x^{1 + 2 x - 1 \cdot 3}$

Step 1.2.4

Multiply $- 1$ by $3$ .

$y = x^{1 + 2 x - 3}$

Step 1.3

Subtract $3$ from $1$ .

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

Step 2

The leading coefficient test requires a polynomial.

Not a polynomial