Algebra Examples

$\frac{x - 4}{x + 5}$

Step 1

Write $\frac{x - 4}{x + 5}$ as an equation.

$y = \frac{x - 4}{x + 5}$

Step 2

Find the x-intercepts.

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Step 2.1

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

$0 = \frac{x - 4}{x + 5}$

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

$x - 4 = 0$

Step 2.2.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(4, 0)$

Step 3

Find the y-intercepts.

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Step 3.1

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

$y = \frac{(0) - 4}{(0) + 5}$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = \frac{0 - 4}{(0) + 5}$

Step 3.2.2

Remove parentheses.

$y = \frac{0 - 4}{0 + 5}$

Step 3.2.3

Remove parentheses.

$y = \frac{(0) - 4}{(0) + 5}$

Step 3.2.4

Simplify $\frac{(0) - 4}{(0) + 5}$ .

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Step 3.2.4.1

Subtract $4$ from $0$ .

$y = \frac{- 4}{0 + 5}$

Step 3.2.4.2

Add $0$ and $5$ .

$y = \frac{- 4}{5}$

Step 3.2.4.3

Move the negative in front of the fraction.

$y = - \frac{4}{5}$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{4}{5})$

Step 4

List the intersections.

x-intercept(s): $(4, 0)$

y-intercept(s): $(0, - \frac{4}{5})$

Step 5