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if x is equal to the square root of 3 plus 1 divided by square root of 3
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if x is equal to the square root of 3 plus 1 divided by square root of...
Explanation of x = √3 + 1 / √3
Given, x = √3 + 1 / √3
Rationalization of denominator
To simplify the given expression, we need to rationalize the denominator, which means we have to get rid of the radical in the denominator by multiplying it with the conjugate of the denominator.
We know that (a + b)(a - b) = a^2 - b^2
Using this identity, we can multiply and divide the expression by (√3 - 1), which is the conjugate of the denominator.
x = (√3 + 1 / √3) * (√3 - 1 / √3 - 1)
x = [(√3)^2 - (1)^2] / (√3 * (√3 - 1))
x = (3 - 1) / (√3 * (√3 - 1))
x = 2 / (√3 * (√3 - 1))
Simplification of expression
We can further simplify the expression by rationalizing the denominator.
We know that (a + b)(a - b) = a^2 - b^2
Using this identity, we can multiply and divide the expression by (√3 + 1), which is the conjugate of the denominator.
x = (2 / (√3 * (√3 - 1))) * (√3 + 1 / √3 + 1)
x = [(2 * (√3 + 1)) / (3 - 1)]
x = (√3 + 1)
Final Answer
Therefore, x = √3 + 1
Conclusion
In conclusion, we can simplify the expression x = √3 + 1 / √3 by rationalizing the denominator and simplifying the expression to get the final answer as x = √3 + 1.
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