Find the x and y Intercepts f(x)=(-5x+10)/(2x^2-8)

$f (x) = \frac{- 5 x + 10}{2 x^{2} - 8}$

Step 1

Find the x-intercepts.

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

$0 = \frac{- 5 x + 10}{2 x^{2} - 8}$

Solve the equation.

Set the numerator equal to zero.

$- 5 x + 10 = 0$

Solve the equation for $x$ .

Subtract $10$ from both sides of the equation.

$- 5 x = - 10$

Divide each term in $- 5 x = - 10$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 10$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 10}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 10}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 5}$

Simplify the right side.

Divide $- 10$ by $- 5$ .

$x = 2$

Exclude the solutions that do not make $0 = \frac{- 5 x + 10}{2 x^{2} - 8}$ 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 $y$ .

$y = \frac{- 5 \cdot 0 + 10}{2 {(0)}^{2} - 8}$

Solve the equation.

Remove parentheses.

$y = \frac{- 5 \cdot 0 + 10}{2 \cdot 0^{2} - 8}$

Remove parentheses.

$y = \frac{- 5 \cdot 0 + 10}{2 {(0)}^{2} - 8}$

Simplify $\frac{- 5 \cdot 0 + 10}{2 {(0)}^{2} - 8}$ .

Cancel the common factor of $- 5 \cdot 0 + 10$ and $2 {(0)}^{2} - 8$ .

Factor $2$ out of $- 5 \cdot 0$ .

$y = \frac{2 (- 5 \cdot 0) + 10}{2 {(0)}^{2} - 8}$

Factor $2$ out of $10$ .

$y = \frac{2 (- 5 \cdot 0) + 2 \cdot 5}{2 {(0)}^{2} - 8}$

Factor $2$ out of $2 (- 5 \cdot 0) + 2 (5)$ .

$y = \frac{2 (- 5 \cdot 0 + 5)}{2 {(0)}^{2} - 8}$

Cancel the common factors.

Factor $2$ out of $2 {(0)}^{2}$ .

$y = \frac{2 (- 5 \cdot 0 + 5)}{2 ({(0)}^{2}) - 8}$

Factor $2$ out of $- 8$ .

$y = \frac{2 (- 5 \cdot 0 + 5)}{2 {(0)}^{2} + 2 \cdot - 4}$

Factor $2$ out of $2 {(0)}^{2} + 2 \cdot - 4$ .

$y = \frac{2 (- 5 \cdot 0 + 5)}{2 ({(0)}^{2} - 4)}$

Cancel the common factor.

$y = \frac{2 (- 5 \cdot 0 + 5)}{2 ({(0)}^{2} - 4)}$

Rewrite the expression.

$y = \frac{- 5 \cdot 0 + 5}{{(0)}^{2} - 4}$

Simplify the numerator.

Multiply $- 5$ by $0$ .

$y = \frac{0 + 5}{0^{2} - 4}$

Add $0$ and $5$ .

$y = \frac{5}{0^{2} - 4}$

Simplify the denominator.

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

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

Subtract $4$ from $0$ .

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

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+10)/(2x^2-8)

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