Find the x and y Intercepts R(x)=(14(x-1))/((x+1)(x+7))

$R (x) = \frac{14 (x - 1)}{(x + 1) (x + 7)}$

Step 1

Find the x-intercepts.

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

$0 = \frac{14 (x - 1)}{(x + 1) (x + 7)}$

Solve the equation.

Set the numerator equal to zero.

$14 (x - 1) = 0$

Solve the equation for $x$ .

Divide each term in $14 (x - 1) = 0$ by $14$ and simplify.

Divide each term in $14 (x - 1) = 0$ by $14$ .

$\frac{14 (x - 1)}{14} = \frac{0}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 (x - 1)}{14} = \frac{0}{14}$

Divide $x - 1$ by $1$ .

$x - 1 = \frac{0}{14}$

Simplify the right side.

Divide $0$ by $14$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{14 ((0) - 1)}{((0) + 1) ((0) + 7)}$

Solve the equation.

Remove parentheses.

$y = \frac{14 (0 - 1)}{((0) + 1) ((0) + 7)}$

Remove parentheses.

$y = \frac{14 (0 - 1)}{(0 + 1) ((0) + 7)}$

Remove parentheses.

$y = \frac{14 (0 - 1)}{(0 + 1) (0 + 7)}$

Remove parentheses.

$y = \frac{14 ((0) - 1)}{((0) + 1) ((0) + 7)}$

Simplify $\frac{14 ((0) - 1)}{((0) + 1) ((0) + 7)}$ .

Reduce the expression by cancelling the common factors.

Cancel the common factor of $14$ and $(0) + 7$ .

Factor $7$ out of $14 ((0) - 1)$ .

$y = \frac{7 (2 ((0) - 1))}{((0) + 1) ((0) + 7)}$

Cancel the common factors.

Factor $7$ out of $((0) + 1) ((0) + 7)$ .

$y = \frac{7 (2 ((0) - 1))}{7 (((0) + 1) (0 + 1))}$

Cancel the common factor.

$y = \frac{7 (2 ((0) - 1))}{7 (((0) + 1) (0 + 1))}$

Rewrite the expression.

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

Cancel the common factor of $(0) - 1$ and $0 + 1$ .

Rewrite $0$ as $- 1 (0)$ .

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

Rewrite $- 1$ as $- 1 (1)$ .

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

Factor $- 1$ out of $- 1 \cdot 0 - 1 \cdot 1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $- 1$ .

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

Simplify the expression.

Add $0$ and $1$ .

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

Divide $- 2$ by $1$ .

$y = - 2$

y-intercept(s) in point form.

y-intercept(s): $(0, - 2)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 2)$

Step 4

Find the x and y Intercepts R(x)=(14(x-1))/((x+1)(x+7))

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