Answer:
So, the expression (3mKs)X²+2/2x²-x-6 is undefined when x is equal to -3/2 or x is equal to 2. These are the values of x for which the expression does not exist.
Explanation:
To find the values of x for which the expression (3mKs)X²+2/2x²-x-6 does not exist, we need to identify the conditions under which the expression is undefined. In this case, the expression is a rational function (a fraction) with a denominator of 2x² - x - 6.
To determine when this expression is undefined, we need to find the values of x that make the denominator equal to zero, because division by zero is undefined in mathematics. So, we need to solve the equation:
2x² - x - 6 = 0
To factor this quadratic equation, we can break it down as follows:
2x² - 4x + 3x - 6 = 0
Now, we factor by grouping:
2x(x - 2) + 3(x - 2) = 0
Now, we can see that (x - 2) is a common factor:
(2x + 3)(x - 2) = 0
Now, we can solve for x by setting each factor equal to zero:
2x + 3 = 0
2x = -3
x = -3/2
x - 2 = 0
x = 2
So, the expression (3mKs)X²+2/2x²-x-6 is undefined when x is equal to -3/2 or x is equal to 2. These are the values of x for which the expression does not exist.