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

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Jun 03, 2024

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Simplifying the Expression (x+3)(x-3)/x^2-6

In this article, we will simplify the algebraic expression (x+3)(x-3)/x^2-6. To simplify this expression, we need to follow the order of operations (PEMDAS) and apply the rules of algebra.

Step 1: Expand the Numerator

The numerator of the expression is (x+3)(x-3). We can expand this expression using the distributive property:

(x+3)(x-3) = x^2 - 3x + 3x - 9

Combine like terms:

= x^2 - 9

Step 2: Simplify the Denominator

The denominator of the expression is x^2 - 6. We can factorize this expression as:

x^2 - 6 = (x + √6)(x - √6)

Step 3: Simplify the Expression

Now, we can rewrite the original expression as:

(x^2 - 9) / ((x + √6)(x - √6))

Step 4: Cancel Out Common Factors

We can see that there are no common factors between the numerator and the denominator. Therefore, the simplified expression is:

(x^2 - 9) / ((x + √6)(x - √6))

And that's the simplified form of the expression (x+3)(x-3)/x^2-6!