Find the x and y Intercepts f(x)=(3x+27)/(x^2+x-72)

$f (x) = \frac{3 x + 27}{x^{2} + x - 72}$

Step 1

Find the x-intercepts.

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

$0 = \frac{3 x + 27}{x^{2} + x - 72}$

Solve the equation.

Set the numerator equal to zero.

$3 x + 27 = 0$

Solve the equation for $x$ .

Subtract $27$ from both sides of the equation.

$3 x = - 27$

Divide each term in $3 x = - 27$ by $3$ and simplify.

Divide each term in $3 x = - 27$ by $3$ .

$\frac{3 x}{3} = \frac{- 27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 27}{3}$

Divide $x$ by $1$ .

$x = \frac{- 27}{3}$

Simplify the right side.

Divide $- 27$ by $3$ .

$x = - 9$

Exclude the solutions that do not make $0 = \frac{3 x + 27}{x^{2} + x - 72}$ 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 $y$ .

$y = \frac{3 (0) + 27}{{(0)}^{2} + 0 - 72}$

Solve the equation.

Remove parentheses.

$y = \frac{3 (0) + 27}{{(0)}^{2} + 0 - 72}$

Remove parentheses.

$y = \frac{3 (0) + 27}{0^{2} + 0 - 72}$

Remove parentheses.

$y = \frac{3 (0) + 27}{{(0)}^{2} + 0 - 72}$

Simplify $\frac{3 (0) + 27}{{(0)}^{2} + 0 - 72}$ .

Simplify the numerator.

Multiply $3$ by $0$ .

$y = \frac{0 + 27}{0^{2} + 0 - 72}$

Add $0$ and $27$ .

$y = \frac{27}{0^{2} + 0 - 72}$

Simplify the denominator.

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

$y = \frac{27}{0 + 0 - 72}$

Add $0$ and $0$ .

$y = \frac{27}{0 - 72}$

Subtract $72$ from $0$ .

$y = \frac{27}{- 72}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $27$ and $- 72$ .

Factor $9$ out of $27$ .

$y = \frac{9 (3)}{- 72}$

Cancel the common factors.

Factor $9$ out of $- 72$ .

$y = \frac{9 \cdot 3}{9 \cdot - 8}$

Cancel the common factor.

$y = \frac{9 \cdot 3}{9 \cdot - 8}$

Rewrite the expression.

$y = \frac{3}{- 8}$

Move the negative in front of the fraction.

$y = - \frac{3}{8}$

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{8})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{3}{8})$

Step 4

Find the x and y Intercepts f(x)=(3x+27)/(x^2+x-72)

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