Simplifying an Algebraic Expression
In this article, we will simplify the algebraic expression:
$\frac{1}{2} + \sqrt{3} + \frac{2}{\sqrt{5}} - \sqrt{3} + \frac{1}{2} - \frac{1}{\sqrt{5}}$
Let's break down the expression and simplify it step by step.
Simplifying the Expression
First, we can combine the like terms:
$\frac{1}{2} + \frac{1}{2} = 1$
This simplifies the expression to:
$1 + \sqrt{3} + \frac{2}{\sqrt{5}} - \sqrt{3} - \frac{1}{\sqrt{5}}$
Next, we can combine the radical terms:
$\sqrt{3} - \sqrt{3} = 0$
This simplifies the expression to:
$1 + \frac{2}{\sqrt{5}} - \frac{1}{\sqrt{5}}$
Now, we can simplify the fraction terms:
$\frac{2}{\sqrt{5}} - \frac{1}{\sqrt{5}} = \frac{2 - 1}{\sqrt{5}} = \frac{1}{\sqrt{5}}$
This simplifies the expression to:
$1 + \frac{1}{\sqrt{5}}$
Final Simplified Expression
The final simplified expression is:
$1 + \frac{1}{\sqrt{5}}$
In conclusion, the simplified expression is a combination of an integer and a fraction with a radical in the denominator.
