(x+1/x-1-x-1/x+1) 2x/5x-5

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Jun 03, 2024

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Simplifying the Expression: (x+1/x-1-x-1/x+1) 2x/5x-5

In this article, we will simplify the given expression: (x+1/x-1-x-1/x+1) 2x/5x-5. To simplify this expression, we will follow the order of operations (PEMDAS) and apply the laws of algebra.

Step 1: Simplify the fraction

Let's start by simplifying the fraction (x+1/x-1-x-1/x+1).

(x+1/x-1-x-1/x+1) = ((x+1)/x - (x+1)/x)

Combine like terms

((x+1)/x - (x+1)/x) = (x/x + 1/x - x/x - 1/x)

= 1/x

So, the simplified fraction is 1/x.

Step 2: Simplify the entire expression

Now, we can simplify the entire expression (1/x) 2x/5x-5.

(1/x) 2x/5x-5 = (2x/5x) - 5/x

Cancel out the x terms

(2x/5x) = 2/5

So, the simplified expression is:

2/5 - 5/x

And that's the final answer!