Solving the Rational Expression: If x^2 - 4 then x^2 - x - 6 / x^2

Understanding the Expression: If x = 2 Then x^2-x-6/x^2-4

The given expression is a mathematical statement that involves the variable x. To evaluate this expression, we need to follow the order of operations, which states that we should perform operations inside the parentheses first, then exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right).

Step 1: Evaluate the Numerator

The numerator of the expression is x^2 - x - 6. We can start by factoring this quadratic expression. We are looking for two numbers whose product is -6 and whose sum is -1. These numbers are 3 and -2. Therefore, we can factor the numerator as follows:

x^2 - x - 6 = (x + 2)(x - 3)

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Now that we have factored the numerator, we can substitute x = 2 into the expression. This will allow us to evaluate the numerator and denominator separately.

Step 2: Evaluate the Denominator

The denominator of the expression is x^2 - 4. We can factor this expression as follows:

x^2 - 4 = (x + 2)(x - 2)

Solved If f(x)=(x2+2)(x2+6), then find and simplify:f'(x)= | Chegg.com

Now that we have factored the denominator, we can substitute x = 2 into the expression. This will allow us to evaluate the numerator and denominator separately.

Step 3: Evaluate the Expression

Now that we have evaluated the numerator and denominator, we can substitute x = 2 into the expression to obtain the final result. We have:

Numerator: (2 + 2)(2 - 3) = (4)(-1) = -4

Denominator: (2 + 2)(2 - 2) = (4)(0) = 0

Since the denominator is zero, we cannot divide by zero. Therefore, the expression is undefined when x = 2.

Conclusion (Implicitly)

When we substitute x = 2 into the expression, we obtain an undefined result. This is because the denominator of the expression is zero when x = 2, and we cannot divide by zero. This demonstrates that the given expression is not defined when x = 2.

Why is the Expression Undefined?

The denominator of the expression is zero when x = 2.
We cannot divide by zero in mathematics.
Therefore, the expression is undefined when x = 2.

What This Means

The fact that the expression is undefined when x = 2 has significant implications. It means that we cannot use this expression to make predictions or draw conclusions about the behavior of the function when x is close to 2. It also means that we need to be careful when substituting values into the expression, as we may encounter undefined results.

Implications for Math and Science

The fact that the expression is undefined when x = 2 has implications for mathematics and science. It means that we need to be careful when using algebraic expressions to model real-world phenomena, as we may encounter undefined results. It also means that we need to be aware of the limitations of mathematical models and use caution when making predictions or drawing conclusions.