Задача 11605 Сократите дробь...

ifiifi3

17.11.2016

Сократите дробь (9-6sqrt(2))/(sqrt(3)-sqrt(6))

SOVA

17.11.2016

★

1.
sqrt(3)-sqrt(6)=sqrt(3)-sqrt(2*3)=sqrt(3)*(1-sqrt(2))

9-6sqrt(2)=3(3-2sqrt(2))

(9-6sqrt(2))/sqrt(3)-sqrt(6)= 3*(3-2sqrt(2))/sqrt(3)*(1-sqrt(2))=sqrt(3)*(3-2sqrt(2))/(1-sqrt(2)).
2.
1)
(sqrt(x)+1)*(sqrt(x)+1)-(sqrt(x)-1)*(sqrt(x)-1)+4sqrt(x)*(x-1))/((sqrt(x))^2-1^2)=

=(x+2sqrt(x)+1-x+2sqrt(x)-1+4sqrt(x)*x-4x)/(x-1)=

=(4sqrt(x)+4xsqrt(x)-4x)/(x-1)

2) sqrt(x) - (1/sqr(x))=(x-1)/sqrt(x)

3)(4sqrt(x)+4xsqrt(x)-4x)/(x-1) * (х-1)/sqrt(x)=

=sqrt(x)*(4+4x-4sqrt(x))/(sqrt(x))=

=4+4x-4sqrt(x).