Question

Select all the correct values in the table.For which values is this expression undefined?1 - 1512 – 21 – 3 2:2 + 21+I = -2I = -1= 0I = 1I = 31 = 5ResetNext

Answer 1

The expression will be undefined if the denominator will be equal to 0.

From the given expression :

`(x-1)/(x^2-2x-3)+(5)/(2x^2+2x)`

If any of the denominator equal to 0, the expression will be undefined

Let's find the value of x that will make the first fraction undefined.

The denominator of the first term is :

`x^2-2x-3=0`

Using factoring :

`\begin{gathered} x^2-2x-3=0 \\ (x+m)(x+n)=0 \end{gathered}`

We need to think of two numbers, m and n that has a product of -3 and a sum of -2

in this case, m must be -3 and n must be 1.

The sum is -2 and the product is -3

`(x-3)(x+1)=0`

Then find the value of x by equating the factors to 0 :

`\begin{gathered} x-3=0\Rightarrow x=3 \\ x+1=0\Rightarrow x=-1 \end{gathered}`

So the values of x that will make the first fraction undefined are -1 and 3

Next is to find the values of x to make the 2nd fraction undefined

`\begin{gathered} 2x^2+2x=0 \\ 2x(x+1)=0 \end{gathered}`

Then equate both factors to 0.

`\begin{gathered} 2x=0\Rightarrow x=0 \\ x+1\Rightarrow x=-1 \end{gathered}`

The values of x that will make the 2nd fraction undefined are 0 and -1

To summarize :

The values of x that will make the whole expression undefined are :

-1, 3 and 0