What is the process to list all numbers for which rational expression is undefined? Ex: y-3divided y+5
Look to see if the expression contains any fractions.
Those fractions cannot be zero, since we cannot divide by zero.
So take each of the fractions and set them equal to zero and solve.
You now have the value of the variable that we cannot use.
in your example,
(y-3)/(y+5)
y+5 = 0
y = -5
so:
(y-3)/(y+5), y ≠ -5
in some cases the could be more than one restriction.
e.g. 5x/(x^2 - x - 6)
x^2 - x - 6 = 0
(x-3)(x+2) = 0
x= 3 or x = -2
So we have :
5x/(x^2 - x - 6) , x ≠-2, 3
To determine the numbers for which a rational expression is undefined, we need to find the values that make the denominator equal to zero since division by zero is undefined.
In this case, the rational expression is (y-3) divided by (y+5). Thus, we need to find the values of y that make the denominator (y+5) equal to zero.
To do this, we can set the denominator equal to zero and solve for y:
y + 5 = 0
Subtracting 5 from both sides:
y = -5
Therefore, the value of y = -5 makes the denominator zero, resulting in an undefined rational expression. So, any number except -5 could be listed as the values for which this rational expression is defined.