Find the x and y Intercepts f(x)=(5x+25)/(x^2+x-20)

$f (x) = \frac{5 x + 25}{x^{2} + x - 20}$

Step 1

Find the x-intercepts.

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

$0 = \frac{5 x + 25}{x^{2} + x - 20}$

Solve the equation.

Set the numerator equal to zero.

$5 x + 25 = 0$

Solve the equation for $x$ .

Subtract $25$ from both sides of the equation.

$5 x = - 25$

Divide each term in $5 x = - 25$ by $5$ and simplify.

Divide each term in $5 x = - 25$ by $5$ .

$\frac{5 x}{5} = \frac{- 25}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 25}{5}$

Divide $x$ by $1$ .

$x = \frac{- 25}{5}$

Simplify the right side.

Divide $- 25$ by $5$ .

$x = - 5$

Exclude the solutions that do not make $0 = \frac{5 x + 25}{x^{2} + x - 20}$ true.

$No solution$

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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

$y = \frac{5 (0) + 25}{{(0)}^{2} + 0 - 20}$

Solve the equation.

Remove parentheses.

$y = \frac{5 (0) + 25}{{(0)}^{2} + 0 - 20}$

Remove parentheses.

$y = \frac{5 (0) + 25}{0^{2} + 0 - 20}$

Remove parentheses.

$y = \frac{5 (0) + 25}{{(0)}^{2} + 0 - 20}$

Simplify $\frac{5 (0) + 25}{{(0)}^{2} + 0 - 20}$ .

Simplify the numerator.

Multiply $5$ by $0$ .

$y = \frac{0 + 25}{0^{2} + 0 - 20}$

Add $0$ and $25$ .

$y = \frac{25}{0^{2} + 0 - 20}$

Simplify the denominator.

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

$y = \frac{25}{0 + 0 - 20}$

Add $0$ and $0$ .

$y = \frac{25}{0 - 20}$

Subtract $20$ from $0$ .

$y = \frac{25}{- 20}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $25$ and $- 20$ .

Factor $5$ out of $25$ .

$y = \frac{5 (5)}{- 20}$

Cancel the common factors.

Factor $5$ out of $- 20$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $None$

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

Step 4

Find the x and y Intercepts f(x)=(5x+25)/(x^2+x-20)

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