What happens when a value causes a denominator in a fraction to be equal to zero?
Responses
The value of the equation becomes zero.
There are infinite solutions.
This value is a solution to the equation.
This fraction is undefined.
This fraction is undefined.
Rewrite the equation (5)/(2x-8)−1=9
as two equations joined by “and.”
(5)/(2x-8)−1=9 and x≠4
(5)/(2x-8)−1=9 and x≠−4
(5)/(2x-8)=9 and x≠−8
(5)/(2x-8)−1=9 and x≠8
(5)/(2x-8)−1=9 and x≠4
What value makes the equation −5=4−(3x)/(4-3x)
undefined?(1 point)
Responses
−3/4
negative Start Fraction 3 over 4 End Fraction
4/3
Start Fraction 4 over 3 End Fraction
3/4
Start Fraction 3 over 4 End Fraction
−4/3
The value that makes the equation undefined is 3/4 (Start Fraction 3 over 4 End Fraction).
When a value causes a denominator in a fraction to be equal to zero, the fraction becomes undefined.
The correct answer is that the fraction becomes undefined when the denominator is equal to zero.
To understand why, let's consider the definition of a fraction. A fraction is a way of representing a division operation, where the numerator is divided by the denominator. Mathematically, we can write a fraction as `a/b`, where `a` is the numerator and `b` is the denominator.
In division, dividing by zero is undefined. This means that there is no meaningful result when you divide a number by zero. It goes against mathematical principles and is not a valid operation.
So, when the denominator in a fraction becomes zero (b = 0), the fraction becomes undefined since division by zero is not possible. It is important to note that this applies to both rational numbers (fractions) and real numbers.
In the context of equations, if a value causes the denominator of a fraction to be zero, it means that this value is not a valid solution to the equation.