-1-2x%2Fx%5E2-1.jpeg "(1/1-x+2/x+1-5-x/1-x^2) 1-2x/x^2-1")
Rational Expression: Simplifying the Complexity
In this article, we will dive into the world of rational expressions and explore the simplification of the complex expression (1/1-x+2/x+1-5-x/1-x^2) / (1-2x/x^2-1). Buckle up and let's get started!
The Given Expression
The given expression is:
(1/1-x+2/x+1-5-x/1-x^2) / (1-2x/x^2-1)
Step 1: Simplify the Numerator
Let's break down the numerator:
1/1-x + 2/x + 1 - 5 - x/1-x^2
Combine like terms:
1 - x + 2/x + 1 - 5 - x/1-x^2
Simplify further:
-3 - x + 2/x - x/1-x^2
Step 2: Simplify the Denominator
The denominator is:
1 - 2x/x^2 - 1
Simplify by combining like terms:
-2x/x^2
Step 3: Simplify the Entire Expression
Now, let's put it all together:
(-3 - x + 2/x - x/1-x^2) / (-2x/x^2)
Simplified Expression
After simplifying, we get:
((x-3)(1-x) + 2 - x^2) / 2x
And there you have it! We have successfully simplified the complex expression (1/1-x+2/x+1-5-x/1-x^2) / (1-2x/x^2-1).
Takeaway
Rational expressions may seem daunting at first, but by breaking them down step by step, we can simplify even the most complex expressions. Remember to combine like terms, cancel out any common factors, and simplify the numerator and denominator separately before putting it all together. Happy simplifying!
