Find the x and y Intercepts f(x)=(3x+30)/(x^2-4x+3)

$f (x) = \frac{3 x + 30}{x^{2} - 4 x + 3}$

Step 1

Find the x-intercepts.

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

$0 = \frac{3 x + 30}{x^{2} - 4 x + 3}$

Solve the equation.

Set the numerator equal to zero.

$3 x + 30 = 0$

Solve the equation for $x$ .

Subtract $30$ from both sides of the equation.

$3 x = - 30$

Divide each term in $3 x = - 30$ by $3$ and simplify.

Divide each term in $3 x = - 30$ by $3$ .

$\frac{3 x}{3} = \frac{- 30}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 30}{3}$

Divide $x$ by $1$ .

$x = \frac{- 30}{3}$

Simplify the right side.

Divide $- 30$ by $3$ .

$x = - 10$

x-intercept(s) in point form.

x-intercept(s): $(- 10, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{3 (0) + 30}{{(0)}^{2} - 4 \cdot 0 + 3}$

Solve the equation.

Remove parentheses.

$y = \frac{3 (0) + 30}{0^{2} - 4 \cdot 0 + 3}$

Remove parentheses.

$y = \frac{3 (0) + 30}{{(0)}^{2} - 4 \cdot 0 + 3}$

Simplify $\frac{3 (0) + 30}{{(0)}^{2} - 4 \cdot 0 + 3}$ .

Simplify the numerator.

Multiply $3$ by $0$ .

$y = \frac{0 + 30}{0^{2} - 4 \cdot 0 + 3}$

Add $0$ and $30$ .

$y = \frac{30}{0^{2} - 4 \cdot 0 + 3}$

Simplify the denominator.

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

$y = \frac{30}{0 - 4 \cdot 0 + 3}$

Multiply $- 4$ by $0$ .

$y = \frac{30}{0 + 0 + 3}$

Add $0$ and $0$ .

$y = \frac{30}{0 + 3}$

Add $0$ and $3$ .

$y = \frac{30}{3}$

Divide $30$ by $3$ .

$y = 10$

y-intercept(s) in point form.

y-intercept(s): $(0, 10)$

Step 3

List the intersections.

x-intercept(s): $(- 10, 0)$

y-intercept(s): $(0, 10)$

Step 4

Find the x and y Intercepts f(x)=(3x+30)/(x^2-4x+3)

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