Find the x and y Intercepts y=((x-4)(x+3))/(x+3)

$y = \frac{(x - 4) (x + 3)}{x + 3}$

Step 1

Find the x-intercepts.

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

$0 = \frac{(x - 4) (x + 3)}{x + 3}$

Solve the equation.

Set the numerator equal to zero.

$(x - 4) (x + 3) = 0$

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 $0$ .

$x - 4 = 0$

$x + 3 = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

The final solution is all the values that make $(x - 4) (x + 3) = 0$ true.

$x = 4, - 3$

Exclude the solutions that do not make $0 = \frac{(x - 4) (x + 3)}{x + 3}$ true.

$x = 4$

x-intercept(s) in point form.

x-intercept(s): $(4, 0)$

Step 2

Find the y-intercepts.

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

$y = \frac{((0) - 4) ((0) + 3)}{(0) + 3}$

Solve the equation.

Remove parentheses.

$y = \frac{(0 - 4) ((0) + 3)}{(0) + 3}$

Remove parentheses.

$y = \frac{(0 - 4) (0 + 3)}{(0) + 3}$

Remove parentheses.

$y = \frac{(0 - 4) (0 + 3)}{0 + 3}$

Remove parentheses.

$y = \frac{((0) - 4) ((0) + 3)}{(0) + 3}$

Simplify $\frac{((0) - 4) ((0) + 3)}{(0) + 3}$ .

Cancel the common factor of $(0) + 3$ .

Cancel the common factor.

$y = \frac{((0) - 4) ((0) + 3)}{(0) + 3}$

Divide $(0) - 4$ by $1$ .

$y = (0) - 4$

Subtract $4$ from $0$ .

$y = - 4$

y-intercept(s) in point form.

y-intercept(s): $(0, - 4)$

Step 3

List the intersections.

x-intercept(s): $(4, 0)$

y-intercept(s): $(0, - 4)$

Step 4

Find the x and y Intercepts y=((x-4)(x+3))/(x+3)

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