Answer and step-by-step explanation:
To make the rational expression undefined, the denominator must be equal to 0.
1. 2/ x + 7
The variable x is only on the denominator so let's equate the denominator to 0.
x + 7 = 0
x + 7 - 7 = 0 - 7
x = -7
Substitute -7 to x to check if it's correct.
2/ -7 + 7
= 2/0
You cannot divide 2 by 0. The answer will be undefined and "Math Error" will appear in your calculator if you try it.
The value of x is -7.
2. 2/ 4x-3
If you substitute any whole numbers to x, the denominator will not be equal to 0. So x must be a fraction. The hint is if you subtract 3 the answer will be 0 and that only means the product of 4 and x must equal to 3.
4x = 3
4x/4 = 3/4
x = 3/4
Then let's see if it's correct.
2/ 4(3/4) - 3
= 2/ 3 - 3
= 2/0
The value of x is 3/4.
3. 4/x
As I said earlier, the answer will be undefined if the denominator is equal to 0.
4/0 = undefined
The value of x is 0.
4. x + 1 / x + 5
In this case, the numerator still does not matter so let's just focus on the denominator.
x + 5 = 0
x + 5 - 5 = 0 - 5
x = -5
Check:
-5 + 1 / -5 + 5
= -4/0
The value of x is -5.
5. 6 - x^2 / x^3
You can use the fact where a zero that is raised to any exponent will always be 0 or 0^x = 0.
[tex] \\ {x}^{3} = 0 \\ \sqrt[3]{ {x}^{3} } = \sqrt[3]{0} \\ x = 0[/tex]
Check:
6 - 0^2 / 0^3
= 6 - 0 / 0
= 6/0
The value of x is 0.
