Question

Find all values of X for which the expression is undefined;

x+5/x^2+x-12

You only need to find what x is/are when the denominator is 0, which is undefined

Answer 1

x= 3 and x= -4.

Explanation:

The only way to make this expression undefined, is if the denominator equals 0. Therefore, let's find out all the values that make the denominator equal 0:

`x^(2) +x-12=0\\\\\\`

Factorize x.

`(x-3)(x+4)=0\\\\x_(1) =3\\\\x_(2) =-4\\`

Therefore, we have 2 values that make this whole expression be undefined: 3 and -4.

Extra. Check out the graph of the fuction and see how it looks when we make x=3 and x= -4 (check image below).

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A good trick to factorize x.

Write this:

(x )(x )

We are looking for 2 numbers that equal 1 when added up, and -12 when multiplied, because the coefficient of x in
`x^(2) +x-12=0\\\\\\` is 1, and the coefficient of -12 is itself.

-3 and 4 are 2 numbers that meet these parameters, therefore, you write:

(x-3)(x+4)

Note. Sometimes it is not possible to factorize x using this method, you will have to use other methods to solve the equation.