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(3+5/x)(9-15/x+25/x^2)

2 min read Jun 16, 2024
(3+5/x)(9-15/x+25/x^2)

Simplifying the Expression (3 + 5/x)(9 - 15/x + 25/x^2)

This article will guide you through the process of simplifying the algebraic expression (3 + 5/x)(9 - 15/x + 25/x^2).

Expanding the Expression

The first step is to expand the expression using the distributive property or FOIL method:

(3 + 5/x)(9 - 15/x + 25/x^2) =

  • 3(9 - 15/x + 25/x^2) + (5/x)(9 - 15/x + 25/x^2)

Now, distribute each term:

  • 27 - 45/x + 75/x^2 + 45/x - 75/x^2 + 125/x^3

Combining Like Terms

Next, identify and combine like terms:

  • 27 + (-45/x + 45/x) + (75/x^2 - 75/x^2) + 125/x^3

This simplifies to:

  • 27 + 125/x^3

Final Simplified Expression

Therefore, the simplified form of the expression (3 + 5/x)(9 - 15/x + 25/x^2) is 27 + 125/x^3.

Important Note: This expression is defined for all real values of x except x = 0, as the denominator cannot be zero.

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