Find the Excluded Values (2x^2-5x-16)/(x^2-x-20)-x/(x+4)

$\frac{2 x^{2} - 5 x - 16}{x^{2} - x - 20} - \frac{x}{x + 4}$

Set the denominator in $\frac{2 x^{2} - 5 x - 16}{x^{2} - x - 20}$ equal to $0$ to find where the expression is undefined.

$x^{2} - x - 20 = 0$

Solve for $x$ .

Factor $x^{2} - x - 20$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 20$ and whose sum is $- 1$ .

$- 5, 4$

Write the factored form using these integers.

$(x - 5) (x + 4) = 0$

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

$x - 5 = 0$

$x + 4 = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

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

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

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

The final solution is all the values that make $(x - 5) (x + 4) = 0$ true.

$x = 5, - 4$

Set the denominator in $\frac{x}{x + 4}$ equal to $0$ to find where the expression is undefined.

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x = - 4, x = 5$

Find the Excluded Values (2x^2-5x-16)/(x^2-x-20)-x/(x+4)

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