Algebra Examples

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

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{x + 1}{(x + 2) (x - 5)}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$x + 1 = 0$

Step 1.2.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 1, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{(0) + 1}{((0) + 2) ((0) - 5)}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{0 + 1}{((0) + 2) ((0) - 5)}$

Step 2.2.2

Remove parentheses.

$y = \frac{0 + 1}{(0 + 2) ((0) - 5)}$

Step 2.2.3

Remove parentheses.

$y = \frac{0 + 1}{(0 + 2) (0 - 5)}$

Step 2.2.4

Remove parentheses.

$y = \frac{(0) + 1}{((0) + 2) ((0) - 5)}$

Step 2.2.5

Simplify $\frac{(0) + 1}{((0) + 2) ((0) - 5)}$ .

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Step 2.2.5.1

Add $0$ and $1$ .

$y = \frac{1}{(0 + 2) (0 - 5)}$

Step 2.2.5.2

Simplify the denominator.

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Step 2.2.5.2.1

Add $0$ and $2$ .

$y = \frac{1}{2 (0 - 5)}$

Step 2.2.5.2.2

Subtract $5$ from $0$ .

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

Step 2.2.5.3

Simplify the expression.

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Step 2.2.5.3.1

Multiply $2$ by $- 5$ .

$y = \frac{1}{- 10}$

Step 2.2.5.3.2

Move the negative in front of the fraction.

$y = - \frac{1}{10}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{10})$

Step 3

List the intersections.

x-intercept(s): $(- 1, 0)$

y-intercept(s): $(0, - \frac{1}{10})$

Step 4