Find the x and y Intercepts y=((x-3)(x+1))/(x-2)

$y = \frac{(x - 3) (x + 1)}{x - 2}$

Find the x-intercepts.

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

$0 = \frac{(x - 3) (x + 1)}{x - 2}$

Solve the equation.

Set the numerator equal to zero.

$(x - 3) (x + 1) = 0$

Solve the equation for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 3 = 0$

$x + 1 = 0$

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make $(x - 3) (x + 1) = 0$ true.

$x = 3, - 1$

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (- 1, 0)$

Find the y-intercepts.

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

$y = \frac{((0) - 3) ((0) + 1)}{(0) - 2}$

Solve the equation.

Remove parentheses.

$y = \frac{(0 - 3) ((0) + 1)}{(0) - 2}$

Remove parentheses.

$y = \frac{(0 - 3) (0 + 1)}{(0) - 2}$

Remove parentheses.

$y = \frac{(0 - 3) (0 + 1)}{0 - 2}$

Remove parentheses.

$y = \frac{((0) - 3) ((0) + 1)}{(0) - 2}$

Simplify $\frac{((0) - 3) ((0) + 1)}{(0) - 2}$ .

Simplify the numerator.

Subtract $3$ from $0$ .

$y = \frac{- 3 (0 + 1)}{0 - 2}$

Add $0$ and $1$ .

$y = \frac{- 3 \cdot 1}{0 - 2}$

Reduce the expression by cancelling the common factors.

Subtract $2$ from $0$ .

$y = \frac{- 3 \cdot 1}{- 2}$

Multiply $- 3$ by $1$ .

$y = \frac{- 3}{- 2}$

Dividing two negative values results in a positive value.

$y = \frac{3}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{3}{2})$

List the intersections.

x-intercept(s): $(3, 0), (- 1, 0)$

y-intercept(s): $(0, \frac{3}{2})$

Find the x and y Intercepts y=((x-3)(x+1))/(x-2)

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