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Sqrt 2 minus sqrt 10/ sqrt 2 plus sqrt 10

I know that the answer is -3/2 + 1/2 sqrt 5 please just show the steps on how to get there thanks

(√2-√10)/(√2+√10)

rationalize the denominator using (a+b)(a-b) = a^2-b^2
(√2-√10)/(√2+√10) * (√2-√10)/(√2-√10)
(√2-√10)^2/(2-10)
(2-2√20+10)/-8
(12-4√5)/-8
-3/2 + √5/2

Did you know?

Did you know that in mathematics, you can simplify expressions involving square roots by rationalizing the denominator? When simplifying: √2 - √10 _____________ √2 + √10 One way to proceed is by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of the denominator, in this case, is: (√2 - √10) So, multiplying the expression by its conjugate: (√2 - √10)(√2 - √10) ____________________ (√2 + √10)(√2 - √10) Expanding this, we get: (2 - 2√10 - 2√10 + 10) ____________________ (2 - √10 + √10 - 10) Simplifying further, (-2√10 + 12) ___________ (-8) Dividing each term by -4, we obtain: (-1/2)√10 + 3/2 Therefore, the simplified expression is: -1/2√10 + 3/2 Isn't it fascinating how manipulating expressions using mathematical techniques can lead to surprising results?