Question

1 \2√3+1 - 1\ 2√3-1​

Answer 1

Ответ:

0

Пошаговое объяснение:

1/2√3 + 1 - 1/2√3 - 1 = 0, потому что все сокращается

Answer 2

To simplify the expression, let's rationalize the denominators.

Given the expression:

$\frac{1}{2\sqrt{3} + 1} - \frac{1}{2\sqrt{3} - 1}$

To rationalize the first fraction in the expression (denominator with $2\sqrt{3} + 1$), we multiply the numerator and denominator by the conjugate of $2\sqrt{3} + 1$, which is $2\sqrt{3} - 1$:

$\frac{1}{2\sqrt{3} + 1} \times \frac{2\sqrt{3} - 1}{2\sqrt{3} - 1} = \frac{2\sqrt{3} - 1}{(2\sqrt{3} + 1)(2\sqrt{3} - 1)}$

Now, to rationalize the second fraction in the expression (denominator with $2\sqrt{3} - 1$), we multiply the numerator and denominator by the conjugate of $2\sqrt{3} - 1$, which is $2\sqrt{3} + 1$:

$\frac{1}{2\sqrt{3} - 1} \times \frac{2\sqrt{3} + 1}{2\sqrt{3} + 1} = \frac{2\sqrt{3} + 1}{(2\sqrt{3} - 1)(2\sqrt{3} + 1)}$

Now, we can combine the two rationalized fractions:

$\frac{2\sqrt{3} - 1}{(2\sqrt{3} + 1)(2\sqrt{3} - 1)} - \frac{2\sqrt{3} + 1}{(2\sqrt{3} - 1)(2\sqrt{3} + 1)}$

Since the denominators are now the same, we can combine the numerators:

$\frac{(2\sqrt{3} - 1) - (2\sqrt{3} + 1)}{(2\sqrt{3} + 1)(2\sqrt{3} - 1)}$

Now, simplify the numerator:

$2\sqrt{3} - 1 - 2\sqrt{3} - 1 = -2$