Find the Excluded Values ((5x^2+10x)/(x^2+2x+1))÷((20x+40)/(x^2-1))

$\frac{5 x^{2} + 10 x}{x^{2} + 2 x + 1} \div \frac{20 x + 40}{x^{2} - 1}$

Step 1

Set the denominator in $\frac{5 x^{2} + 10 x}{x^{2} + 2 x + 1}$ equal to $0$ to find where the expression is undefined.

$x^{2} + 2 x + 1 = 0$

Step 2

Solve for $x$ .

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

$x^{2} + 2 x + 1^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 x = 2 \cdot x \cdot 1$

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot 1 + 1^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 1$ .

${(x + 1)}^{2} = 0$

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 3

Set the denominator in $\frac{20 x + 40}{x^{2} - 1}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 1 = 0$

Step 4

Solve for $x$ .

Add $1$ to both sides of the equation.

$x^{2} = 1$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x = \pm 1$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 1$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 1$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 1$

Step 5

Set the denominator in $\frac{\frac{5 x^{2} + 10 x}{x^{2} + 2 x + 1}}{\frac{20 x + 40}{x^{2} - 1}}$ equal to $0$ to find where the expression is undefined.

$\frac{20 x + 40}{x^{2} - 1} = 0$

Step 6

Solve for $x$ .

Set the numerator equal to zero.

$20 x + 40 = 0$

Solve the equation for $x$ .

Subtract $40$ from both sides of the equation.

$20 x = - 40$

Divide each term in $20 x = - 40$ by $20$ and simplify.

Divide each term in $20 x = - 40$ by $20$ .

$\frac{20 x}{20} = \frac{- 40}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 x}{20} = \frac{- 40}{20}$

Divide $x$ by $1$ .

$x = \frac{- 40}{20}$

Simplify the right side.

Divide $- 40$ by $20$ .

$x = - 2$

Step 7

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 $0$ .

$x = - 2, x = - 1, x = 1$

Step 8

Find the Excluded Values ((5x^2+10x)/(x^2+2x+1))÷((20x+40)/(x^2-1))

Related Questions

Support LCMGCF.com by disabling your adblocker.