For what values of x is the following expression: 1/(x^2-25). How do you solve and determined the undefined value? Thanks!
(x^2-25)=0
Get the square root of x^2-25
=(X-5)(X+5)
5 -5
the expression has to be an equation, equal to something. In the cool rich response, it is wrong. the expression X^2-25=0 cannot ever be here, as the expression has that in the denominator, and division by zero is never allowed.
I think your question left out an important word. Did you mean to write:
<<For what values of x is the following expression undefined?
1/(x^2-25).>>
The answer to THAT question is the two values of x for which the denominator is zero.
To find the values of x for which the expression 1/(x^2-25) is undefined, we need to determine when the denominator, x^2-25, equals zero since division by zero is undefined.
First, we set the denominator equal to zero and solve for x:
x^2 - 25 = 0
Next, we can factor the equation as a difference of squares:
(x - 5)(x + 5) = 0
Now, we can apply the zero product property:
(x - 5) = 0 or (x + 5) = 0
Solving each equation separately gives us two potential values for x:
For (x - 5) = 0, we add 5 to both sides:
x = 5
For (x + 5) = 0, we subtract 5 from both sides:
x = -5
Therefore, the expression 1/(x^2-25) is undefined for x = 5 and x = -5, as plugging these values into the denominator would result in division by zero.