Find the x and y Intercepts f(x)=(5x+25)/(3x^2+16x+5)

$f (x) = \frac{5 x + 25}{3 x^{2} + 16 x + 5}$

Step 1

Find the x-intercepts.

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

$0 = \frac{5 x + 25}{3 x^{2} + 16 x + 5}$

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 $0 = \frac{5 x + 25}{3 x^{2} + 16 x + 5}$ 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 $y$ .

$y = \frac{5 (0) + 25}{3 {(0)}^{2} + 16 (0) + 5}$

Solve the equation.

Remove parentheses.

$y = \frac{5 (0) + 25}{3 \cdot 0^{2} + 16 (0) + 5}$

Remove parentheses.

$y = \frac{5 (0) + 25}{3 {(0)}^{2} + 16 (0) + 5}$

Simplify $\frac{5 (0) + 25}{3 {(0)}^{2} + 16 (0) + 5}$ .

Simplify the numerator.

Multiply $5$ by $0$ .

$y = \frac{0 + 25}{3 \cdot 0^{2} + 16 (0) + 5}$

Add $0$ and $25$ .

$y = \frac{25}{3 \cdot 0^{2} + 16 (0) + 5}$

Simplify the denominator.

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

$y = \frac{25}{3 \cdot 0 + 16 (0) + 5}$

Multiply $3$ by $0$ .

$y = \frac{25}{0 + 16 (0) + 5}$

Multiply $16$ by $0$ .

$y = \frac{25}{0 + 0 + 5}$

Add $0$ and $0$ .

$y = \frac{25}{0 + 5}$

Add $0$ and $5$ .

$y = \frac{25}{5}$

Divide $25$ by $5$ .

$y = 5$

y-intercept(s) in point form.

y-intercept(s): $(0, 5)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 5)$

Step 4

Find the x and y Intercepts f(x)=(5x+25)/(3x^2+16x+5)

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