Question

сократите дроби а²-3/а+√3
5-√5/√5
√в-√с/в-с

Answer 1

$frac{a^2-3}{a+ sqrt{3} } = frac{(a- sqrt{3})(a+ sqrt{3} ) }{a+ sqrt{3} } = a- sqrt{3} \ \ frac{5- sqrt{5} }{ sqrt{5} } = frac{ sqrt{5} ( sqrt{5}-1) }{ sqrt{5} } = sqrt{5} -1 \ \ frac{ sqrt{b} - sqrt{c} }{b-c} = frac{ sqrt{b} - sqrt{c} }{(sqrt{b} - sqrt{c}) (sqrt{b} + sqrt{c}) }= frac{1}{sqrt{b} + sqrt{c}}$

Answer 2

1. (а²-3)/(а+√3) =
((a-√3)(a+√3))/(a+√3) =
a-√3;
2. (5-√5)/√5 =
(√5(5-√5))/5 =
(5√5-5)/5 =
5(√5-1)/5 =
√5-1;
3. (√b-√c)/(b-c) =
(√b-√c)/((√b-√c)(√b+√c)) =
1/(√b+√c)