to find value of x and discontinous 9x²-3x-2/3x²+13x-4
3x^2+13x-4 = 0 when x = -1/6 (13±√217)
9x^2-3x-2 = (3x-2)(3x+1)
so, f(x) is discontinuous at x = -1/6 (13±√217) where the denominator is zero.
To find the values of x and determine the discontinuity, we need to analyze the expression 9x² - 3x - 2 / 3x² + 13x - 4.
Step 1: Factorize the numerator and denominator:
The numerator can be factored as (3x + 2)(3x - 1).
The denominator can be factored as (3x - 1)(x + 4).
So, the expression becomes [(3x + 2)(3x - 1)] / [(3x - 1)(x + 4)].
Step 2: Cancel out any common factors:
We can cancel out the (3x - 1) terms both in the numerator and denominator.
The expression simplifies to (3x + 2) / (x + 4).
Step 3: Determine the value(s) of x that make the expression undefined:
To find the discontinuity, we need to identify the value(s) of x that result in division by zero. In this case, the expression is undefined when the denominator is equal to zero.
So, we set the denominator to zero: x + 4 = 0.
Solving for x, we get x = -4.
Therefore, x = -4 is the value at which the expression is discontinuous.
To summarize:
- The values of x that make the expression undefined (discontinuity): x = -4.
- The simplified expression after factoring and canceling common terms: (3x + 2) / (x + 4).