Find the x and y Intercepts f(x)=(5x-10)/(x^2-3x+2)

$f (x) = \frac{5 x - 10}{x^{2} - 3 x + 2}$

Step 1

Find the x-intercepts.

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

$0 = \frac{5 x - 10}{x^{2} - 3 x + 2}$

Solve the equation.

Set the numerator equal to zero.

$5 x - 10 = 0$

Solve the equation for $x$ .

Add $10$ to 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 $0 = \frac{5 x - 10}{x^{2} - 3 x + 2}$ 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 $y$ .

$y = \frac{5 (0) - 10}{{(0)}^{2} - 3 \cdot 0 + 2}$

Solve the equation.

Remove parentheses.

$y = \frac{5 (0) - 10}{0^{2} - 3 \cdot 0 + 2}$

Remove parentheses.

$y = \frac{5 (0) - 10}{{(0)}^{2} - 3 \cdot 0 + 2}$

Simplify $\frac{5 (0) - 10}{{(0)}^{2} - 3 \cdot 0 + 2}$ .

Simplify the numerator.

Multiply $5$ by $0$ .

$y = \frac{0 - 10}{0^{2} - 3 \cdot 0 + 2}$

Subtract $10$ from $0$ .

$y = \frac{- 10}{0^{2} - 3 \cdot 0 + 2}$

Simplify the denominator.

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

$y = \frac{- 10}{0 - 3 \cdot 0 + 2}$

Multiply $- 3$ by $0$ .

$y = \frac{- 10}{0 + 0 + 2}$

Add $0$ and $0$ .

$y = \frac{- 10}{0 + 2}$

Add $0$ and $2$ .

$y = \frac{- 10}{2}$

Divide $- 10$ by $2$ .

$y = - 5$

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-10)/(x^2-3x+2)

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