Chapter R.6, Problem 1YT

To determine

To calculate: The numbers for which the rational expression $\frac{x-7}{2x^2+4x}$ is undefined.

Answer to Problem 1YT

Solution:

The numbers for which the rational expression $\frac{x-7}{2x^2+4x}$ is undefined are $x=-2$ and $x=0\_$.

Explanation of Solution

Given Information:

The provided rational expression is $\frac{x-7}{2x^2+4x}$.

Formula used:

There are following steps to find the value of the variables for which the rational expression is undefined:

Step 1: Set the denominator of the expression as 0.

Step 2: Solve for the variable.

Calculation:

Consider the provided rational expression:

$\frac{x-7}{2x^2+4x}$

Set the denominator of the rational expression as 0:

$2x^2+4x=0$

Factor the terms as follows:

$2x\left(x+2\right)=0$

As, zero product rule is,

If, $\left(x+a\right)\left(x+b\right)=0$

Then, $\left(x+a\right)=0\text{ or }\left(x+b\right)=0$

Apply the principle of zero products on $2x\left(x+2\right)=0$:

$2x=0$ or $\left(x+2\right)=0$.

Thus, $x=0$ or $x=-2$.

If the variable $x$ is replaced with 0 or $-2$, the denominator becomes 0.

Thus, the rational expression $\frac{x-7}{2x^2+4x}$ is undefined for $x=0$ and $x=-2$.