Question

Упростите выражение: (√5 - √3) / (√5 + √3) - (√5 + √3) / (√5 - √3)=

Answer 1

=√2/√8-√8/√2=√2/√8-√4=√2/√2=1

Answer 2

I can help you with math problems. To simplify the expression, you need to use the following steps:

1. Multiply the numerator and denominator of each fraction by the conjugate of the denominator. The conjugate of a binomial is obtained by changing the sign of the second term. For example, the conjugate of $\sqrt{5}+\sqrt{3}$ is $\sqrt{5}-\sqrt{3}$. 2. Use the difference of squares formula to simplify the denominators. The formula is $(a+b)(a-b)=a^2-b^2$. For example, $(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})=\sqrt{5}^2-\sqrt{3}^2=5-3=2$. 3. Combine the numerators of the fractions by subtracting them. For example, $(\sqrt{5}-\sqrt{3})^2-(\sqrt{5}+\sqrt{3})^2=(5-6\sqrt{15}+3)-(5+6\sqrt{15}+3)=-12\sqrt{15}-4$. 4. Simplify the final fraction by dividing the numerator and denominator by the greatest common factor. The greatest common factor of $-12\sqrt{15}-4$ and $4$ is $4$. Therefore, the final fraction is $\frac{-12\sqrt{15}-4}{4}=\frac{-3\sqrt{15}-1}{1}$.

The final answer is $\frac{-3\sqrt{15}-1}{1}$. You can check your answer by plugging it into a calculator or using an online tool.

: https://www.wolframalpha.com/input/?i=%28%5Csqrt%7B5%7D-%5Csqrt%7B3%7D%29%2F%28%5Csqrt%7B5%7D%2B%5Csqrt%7B3%7D%29-%28%5Csqrt%7B5%7D%2B%5Csqrt%7B3%7D%29%2F%28%5Csqrt%7B5%7D-%5Csqrt%7B3%7D%29%3D Ответь+подробно.+Упростите+выражение:+(√5+-+√3)+/+(√5+++√3)+-+(√5+++√3)+/+(√5+-+√3)=