(x-7) X^2-14x+49/x+7

Jasonbradley

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Jun 17, 2024

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Simplifying the Rational Expression: (x-7)x^2 - 14x + 49 / x + 7

This article will guide you through simplifying the rational expression: (x-7)x^2 - 14x + 49 / x + 7.

Understanding the Expression

The expression is a rational expression because it involves a ratio of two polynomials:

• Numerator: (x-7)x^2 - 14x + 49
• Denominator: x + 7

Simplifying the Expression

To simplify the expression, we can use the following steps:

1. Factor the numerator: The numerator is a quadratic expression. We can factor it by recognizing that it is a perfect square trinomial:

   (x-7)x^2 - 14x + 49 = (x-7)(x^2 - 2*7x + 7^2) = (x-7)(x-7)^2 = (x-7)^3

2. Simplify the expression: Now, the expression becomes:

   (x-7)^3 / (x+7)

3. Check for common factors: There are no common factors between the numerator and denominator, therefore the expression is already in its simplest form.

Conclusion

The simplified form of the rational expression (x-7)x^2 - 14x + 49 / x + 7 is (x-7)^3 / (x+7). It's important to note that this simplified expression is equivalent to the original expression for all values of x except x = -7. This is because the denominator becomes zero when x = -7, making the expression undefined.