Algebra Examples

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

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

Remove parentheses.

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

Step 2.3

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

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Step 2.3.1

Simplify the numerator.

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Step 2.3.1.1

Raise $- 2$ to the power of $2$ .

$y = \frac{4 + 1}{- 2 + 1}$

Step 2.3.1.2

Add $4$ and $1$ .

$y = \frac{5}{- 2 + 1}$

Step 2.3.2

Simplify the expression.

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Step 2.3.2.1

Add $- 2$ and $1$ .

$y = \frac{5}{- 1}$

Step 2.3.2.2

Divide $5$ by $- 1$ .

$y = - 5$

Step 3

Substitute $0$ for $x$ and find the result for $y$ .

$y = \frac{{(0)}^{2} + 1}{(0) + 1}$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = \frac{0^{2} + 1}{(0) + 1}$

Step 4.2

Remove parentheses.

$y = \frac{0^{2} + 1}{0 + 1}$

Step 4.3

Remove parentheses.

$y = \frac{{(0)}^{2} + 1}{(0) + 1}$

Step 4.4

Simplify $\frac{{(0)}^{2} + 1}{(0) + 1}$ .

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Step 4.4.1

Simplify the numerator.

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Step 4.4.1.1

Raising $0$ to any positive power yields $0$ .

$y = \frac{0 + 1}{0 + 1}$

Step 4.4.1.2

Add $0$ and $1$ .

$y = \frac{1}{0 + 1}$

Step 4.4.2

Simplify the expression.

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Step 4.4.2.1

Add $0$ and $1$ .

$y = \frac{1}{1}$

Step 4.4.2.2

Divide $1$ by $1$ .

$y = 1$

Step 5

Substitute $1$ for $x$ and find the result for $y$ .

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

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

Step 6.2

Remove parentheses.

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

Step 6.3

Remove parentheses.

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

Step 6.4

Simplify $\frac{{(1)}^{2} + 1}{(1) + 1}$ .

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Step 6.4.1

Simplify the numerator.

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Step 6.4.1.1

One to any power is one.

$y = \frac{1 + 1}{1 + 1}$

Step 6.4.1.2

Add $1$ and $1$ .

$y = \frac{2}{1 + 1}$

Step 6.4.2

Simplify the expression.

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Step 6.4.2.1

Add $1$ and $1$ .

$y = \frac{2}{2}$

Step 6.4.2.2

Divide $2$ by $2$ .

$y = 1$

Step 7

Substitute $2$ for $x$ and find the result for $y$ .

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

Remove parentheses.

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

Step 8.3

Remove parentheses.

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

Step 8.4

Simplify $\frac{{(2)}^{2} + 1}{(2) + 1}$ .

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Step 8.4.1

Simplify the numerator.

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Step 8.4.1.1

Raise $2$ to the power of $2$ .

$y = \frac{4 + 1}{2 + 1}$

Step 8.4.1.2

Add $4$ and $1$ .

$y = \frac{5}{2 + 1}$

Step 8.4.2

Add $2$ and $1$ .

$y = \frac{5}{3}$

Step 9

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - 5 \\ 0 & 1 \\ 1 & 1 \\ 2 & \frac{5}{3} \end{array}$

Step 10