Question

ребят жаю много баллов. плиз помогите

Answer 1

1
$(ab^{-1}-a^{-1}b)(a^{-1}-b^{-1})^{-2}* frac{1}{ab}=( frac{a}{b}- frac{b}{a} )* frac{1}{( frac{1}{a}- frac{1}{b} )^2} * frac{1}{ab}=$
$= frac{a^2-b^2}{ab} * frac{1}{( frac{b-a}{ab} )^2}* frac{1}{ab} = frac{(a-b)(a+b)}{(ab)^2* frac{(a-b)^2}{(ab)^2} } = frac{a+b}{a-b}.$
2
$frac{ sqrt{12}+3 sqrt{27}- sqrt{75} }{2} = frac{ sqrt{2^2*3}+ 3sqrt{3^2*3}- sqrt{5^2*3} }{2} = frac{ 2sqrt{3}+9 sqrt{3}- 5 sqrt{3} }{2} = frac{(2+9-5)* sqrt{3} }{2} =$ = три корня из трёх.
3
$frac{1}{ 5sqrt{2} -7} - frac{2}{ 3sqrt{2} -4} - frac{2}{1+ sqrt{2} } =$
$=frac{5sqrt{2} +7}{ (5sqrt{2} -7)(5sqrt{2} +7)} - frac{2(3sqrt{2} +4)}{ (3sqrt{2} -4)(3sqrt{2} +4)} - frac{2(1- sqrt{2} )}{(1+ sqrt{2})(1- sqrt{2} )} =$
$=frac{5sqrt{2} +7}{ 50-49} - frac{2(3sqrt{2} +4)}{ 18-16} - frac{2(1- sqrt{2} )}{1-2} )}=5sqrt{2} +7-(3sqrt{2} +4)+(1- sqrt{2} )=$
$=sqrt{2} +4.$