Вправи 501 - 595 » 522

Скоротіть дріб: 1) (x-25)/(√x- 5) = ((√x )^2- 5^2)/(√x- 5) = (√x- 5)(√x+ 5)/(√x- 5) = √x + 5; 2) (√a+ 2)/(a-4) = (√a+ 2)/((√a )^2- 2^2 ) = ((√a+ 2))/((√a- 2)(√a+ 2)) = 1/(√a- 2); 3) (a-3)/(√a+ √3) = ((√a )^2- (√b )^2)/(√a+ √3) = ((√a- √3)(√a+ √3))/((√a+ √3)) = √a – √3; 4) (√10+ √5)/√5 = (√5 • √2 + √5)/√5 = (√5(√2+ 1))/√5 = √2 + 1; 5) (23- √23)/√23 = ((√23 )^2 - √23)/√23 = (√23(√23- 1))/√23 = √23 – 1; 6) (√24- √28)/(√54- √63) = (√(4 • 6)- √(4 • 7))/(√(9 • 6)- √(9 • 7)) = (2√6- 2√7)/(3√6- 3√7) = (2(√6- √7))/(3(√6- √7)) = 2/3; 7) (√a - √b)/(a - 2√ab + b) = (√a- √b)/((√b )^2 - 2√a • √b + (√b )^2 ) = ((√a - √b))/((√a - √b )^2 ) = 1/(√a- √b); 8) (b - 8√b + 16)/(√(b )- 4) = ((√b )^2- 2 • 4√b + 4^2)/(√(b )- 4) = ((√b - 4)^2)/((√b - 4)) = √b – 4.