Graph Using a Table of Values f(x)=(5x+15)/(x^2+2x-15)

$f (x) = \frac{5 x + 15}{x^{2} + 2 x - 15}$

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = \frac{5 (- 2) + 15}{{(- 2)}^{2} + 2 (- 2) - 15}$

Simplify $\frac{5 (- 2) + 15}{{(- 2)}^{2} + 2 (- 2) - 15}$ .

Simplify the numerator.

Multiply $5$ by $- 2$ .

$y = \frac{- 10 + 15}{{(- 2)}^{2} + 2 (- 2) - 15}$

Add $- 10$ and $15$ .

$y = \frac{5}{{(- 2)}^{2} + 2 (- 2) - 15}$

Simplify the denominator.

Raise $- 2$ to the power of $2$ .

$y = \frac{5}{4 + 2 (- 2) - 15}$

Multiply $2$ by $- 2$ .

$y = \frac{5}{4 - 4 - 15}$

Subtract $4$ from $4$ .

$y = \frac{5}{0 - 15}$

Subtract $15$ from $0$ .

$y = \frac{5}{- 15}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $5$ and $- 15$ .

Factor $5$ out of $5$ .

$y = \frac{5 (1)}{- 15}$

Cancel the common factors.

Factor $5$ out of $- 15$ .

$y = \frac{5 \cdot 1}{5 \cdot - 3}$

Cancel the common factor.

$y = \frac{5 \cdot 1}{5 \cdot - 3}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = \frac{5 (- 1) + 15}{{(- 1)}^{2} + 2 (- 1) - 15}$

Simplify $\frac{5 (- 1) + 15}{{(- 1)}^{2} + 2 (- 1) - 15}$ .

Simplify the numerator.

Multiply $5$ by $- 1$ .

$y = \frac{- 5 + 15}{{(- 1)}^{2} + 2 (- 1) - 15}$

Add $- 5$ and $15$ .

$y = \frac{10}{{(- 1)}^{2} + 2 (- 1) - 15}$

Simplify the denominator.

Raise $- 1$ to the power of $2$ .

$y = \frac{10}{1 + 2 (- 1) - 15}$

Multiply $2$ by $- 1$ .

$y = \frac{10}{1 - 2 - 15}$

Subtract $2$ from $1$ .

$y = \frac{10}{- 1 - 15}$

Subtract $15$ from $- 1$ .

$y = \frac{10}{- 16}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $10$ and $- 16$ .

Factor $2$ out of $10$ .

$y = \frac{2 (5)}{- 16}$

Cancel the common factors.

Factor $2$ out of $- 16$ .

$y = \frac{2 \cdot 5}{2 \cdot - 8}$

Cancel the common factor.

$y = \frac{2 \cdot 5}{2 \cdot - 8}$

Rewrite the expression.

$y = \frac{5}{- 8}$

Move the negative in front of the fraction.

$y = - \frac{5}{8}$

Substitute $0$ for $x$ and find the result for $y$ .

$y = \frac{5 (0) + 15}{{(0)}^{2} + 2 (0) - 15}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{5 (0) + 15}{0^{2} + 2 (0) - 15}$

Remove parentheses.

$y = \frac{5 (0) + 15}{{(0)}^{2} + 2 (0) - 15}$

Simplify $\frac{5 (0) + 15}{{(0)}^{2} + 2 (0) - 15}$ .

Simplify the numerator.

Multiply $5$ by $0$ .

$y = \frac{0 + 15}{0^{2} + 2 (0) - 15}$

Add $0$ and $15$ .

$y = \frac{15}{0^{2} + 2 (0) - 15}$

Simplify the denominator.

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

$y = \frac{15}{0 + 2 (0) - 15}$

Multiply $2$ by $0$ .

$y = \frac{15}{0 + 0 - 15}$

Add $0$ and $0$ .

$y = \frac{15}{0 - 15}$

Subtract $15$ from $0$ .

$y = \frac{15}{- 15}$

Divide $15$ by $- 15$ .

$y = - 1$

Substitute $1$ for $x$ and find the result for $y$ .

$y = \frac{5 (1) + 15}{{(1)}^{2} + 2 (1) - 15}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{5 (1) + 15}{1^{2} + 2 (1) - 15}$

Remove parentheses.

$y = \frac{5 (1) + 15}{{(1)}^{2} + 2 (1) - 15}$

Simplify $\frac{5 (1) + 15}{{(1)}^{2} + 2 (1) - 15}$ .

Simplify the numerator.

Multiply $5$ by $1$ .

$y = \frac{5 + 15}{1^{2} + 2 (1) - 15}$

Add $5$ and $15$ .

$y = \frac{20}{1^{2} + 2 (1) - 15}$

Simplify the denominator.

One to any power is one.

$y = \frac{20}{1 + 2 (1) - 15}$

Multiply $2$ by $1$ .

$y = \frac{20}{1 + 2 - 15}$

Add $1$ and $2$ .

$y = \frac{20}{3 - 15}$

Subtract $15$ from $3$ .

$y = \frac{20}{- 12}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $20$ and $- 12$ .

Factor $4$ out of $20$ .

$y = \frac{4 (5)}{- 12}$

Cancel the common factors.

Factor $4$ out of $- 12$ .

$y = \frac{4 \cdot 5}{4 \cdot - 3}$

Cancel the common factor.

$y = \frac{4 \cdot 5}{4 \cdot - 3}$

Rewrite the expression.

$y = \frac{5}{- 3}$

Move the negative in front of the fraction.

$y = - \frac{5}{3}$

Substitute $2$ for $x$ and find the result for $y$ .

$y = \frac{5 (2) + 15}{{(2)}^{2} + 2 (2) - 15}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{5 (2) + 15}{2^{2} + 2 (2) - 15}$

Remove parentheses.

$y = \frac{5 (2) + 15}{{(2)}^{2} + 2 (2) - 15}$

Simplify $\frac{5 (2) + 15}{{(2)}^{2} + 2 (2) - 15}$ .

Simplify the numerator.

Multiply $5$ by $2$ .

$y = \frac{10 + 15}{2^{2} + 2 (2) - 15}$

Add $10$ and $15$ .

$y = \frac{25}{2^{2} + 2 (2) - 15}$

Simplify the denominator.

Raise $2$ to the power of $2$ .

$y = \frac{25}{4 + 2 (2) - 15}$

Multiply $2$ by $2$ .

$y = \frac{25}{4 + 4 - 15}$

Add $4$ and $4$ .

$y = \frac{25}{8 - 15}$

Subtract $15$ from $8$ .

$y = \frac{25}{- 7}$

Move the negative in front of the fraction.

$y = - \frac{25}{7}$

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - \frac{1}{3} \\ - 1 & - \frac{5}{8} \\ 0 & - 1 \\ 1 & - \frac{5}{3} \\ 2 & - \frac{25}{7} \end{array}$

Graph Using a Table of Values f(x)=(5x+15)/(x^2+2x-15)

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