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Simplifying Algebraic Expressions: A Step-by-Step Guide
In this article, we will delve into the world of algebraic expressions and explore how to simplify the expression 1-6x/x-2+9x+4/x+2=x(3x-2)+1/x^2-4. Buckle up and let's get started!
Step 1: Simplify the Left-Hand Side (LHS)
The LHS of the equation is 1-6x/x-2+9x+4/x+2. To simplify this expression, we need to follow the order of operations (PEMDAS):
Simplify the fractions
- 1-6x/x = 1 - 6
- 4/x+2 = 4/x + 2
Combine like terms
- -6x + 9x = 3x
- 1 + 2 = 3
So, the simplified LHS is 3 + 3x + 4/x.
Step 2: Simplify the Right-Hand Side (RHS)
The RHS of the equation is x(3x-2)+1/x^2-4. Let's break it down:
Expand the parentheses
- x(3x-2) = 3x^2 - 2x
Simplify the fraction
- 1/x^2 = x^(-2)
Combine like terms
- 3x^2 - 2x + x^(-2) - 4
So, the simplified RHS is 3x^2 - 2x + x^(-2) - 4.
Comparing the Simplified Expressions
Now that we have simplified both sides of the equation, we can compare them:
3 + 3x + 4/x = 3x^2 - 2x + x^(-2) - 4
Conclusion
In this article, we have successfully simplified the algebraic expression 1-6x/x-2+9x+4/x+2=x(3x-2)+1/x^2-4. By following the order of operations and combining like terms, we were able to rewrite the equation in a more simplified form. This exercise demonstrates the importance of careful manipulation of algebraic expressions to uncover their underlying structure.
