For which values of x is the expression undefined?
start fraction, x, plus, 4, divided by, x, minus, 6, end fraction
x−6
x+4
The expression is undefined when the denominator (x-6) is equal to 0.
So, x - 6 = 0
Solving for x, we get:
x = 6
Therefore, the expression is undefined when x = 6.
To determine the values of x for which the expression is undefined, we need to identify any values of x that would make the denominator of the expression equal to zero. This is because division by zero is undefined in mathematics.
In this case, the expression is (x + 4)/(x - 6). So, we need to find when the denominator, x - 6, equals zero.
To find these values, we can set the denominator equal to zero and solve for x:
x - 6 = 0
Adding 6 to both sides of the equation, we get:
x = 6
Therefore, the expression is undefined when x is equal to 6, since this would make the denominator zero. For any other value of x, the expression is defined.
The expression is undefined when a denominator equals zero since division by zero is undefined.
To find the values of x for which the expression is undefined, we set the denominators equal to zero and solve for x.
For x - 6 = 0, adding 6 to both sides of the equation gives x = 6.
For x + 4 = 0, subtracting 4 from both sides of the equation gives x = -4.
Therefore, the expression is undefined when x = 6 and x = -4.