What are the excluded values?
2/x(x-3)
these are the answer choices.
x = 0 and 3
x = 0 and 2
x = -3 and 3
none of the above
Well, the excluded values are like the unpopular kids at a birthday party - they're just not allowed to join in on the fun! In this case, we need to find the values of x that make the expression undefined.
To do that, we look for any values of x that would make the denominator equal to zero. In this case, since we have x(x-3) in the denominator, we need to find the values of x that would make either x or (x-3) equal to zero.
So, the excluded values would be x = 0 and x = 3. They're a bit like the wallflowers at a dance - they just can't get on the dance floor!
To find the excluded values in the expression 2/x(x-3), we need to look for the values of x that would make the denominator equal to zero. Division by zero is undefined in mathematics, so those values need to be excluded.
In this case, we have two factors in the denominator: x and (x-3). To find the excluded values, we set each factor equal to zero and solve for x:
x = 0
x - 3 = 0
Solving the first equation, we find x = 0.
Solving the second equation, we find x = 3.
Therefore, the excluded values for the expression 2/x(x-3) are x = 0 and x = 3. These values would make the denominator equal to zero.
According to your given choices, I suspect you meant
2/( x(x-3) )
so the restrictions are,
x = 0
x = 3
namely, those values which make the denominator zero, thus resulting in an undefined answer.