Вправи 501 - 595 » 521

Скоротіть дріб: 1) (a^2- 7)/(a+ √7) = (a^2- (√7 )^2)/(a+ √7) = ((a- √7)(a+ √7))/(a+ √7) = a – √7; 2) (√3- b)/(3- b^2 ) = (√3- b)/((√3 )^2- b^2 ) = ((√3- b))/((√3- b)(√3+ b)) = 1/(√3+ b); 3) (c-9)/(√c- 3) = ((√c )^2- 3^2)/(√c- 3) = ((√c- 3)(√c+ 3))/(√c- 3) = √c + 3; 4) (a-b)/(√a+ √b) = ((√a )^2- (√b )^2)/(√a+ √b) = ((√a- √b)(√a+ √b))/((√a+ √b)) = √a – √b; 5) (5√a- 7√b)/(25a-49b) = (5√a- 7√b)/((5√a )^2- (7√b )^2 ) = ((5√a- 7√b))/((5√a- 7√b)(5√a+ 7√b)) = 1/(5√a+ 7√b); 6) (100a^2- 9b)/(10a+3√b) = ((10a)^2- (3√b )^2)/(10a+3√b) = ((10a-3√b)(10a+3√b))/((10a+3√b)) = 10a – 3√b; 7) (√2 - 1)/(√(6 )- √3) = (√(2 )- 1)/(√3 • √2 - √3) = ((√2 - 1))/(√3(√2- 1)) = 1/√3 = √3/((√3 )^2 ) = √3/3; 8) (√35 + √10)/(√7 + √2) = (√7 • √5 + √5 • √2)/(√7 + √2) = (√5 (√7+ √2))/((√7+ √2) ) = √5; 9) (√(15 )- √6)/(5 - √10) = (√5 • √3 - √3 • √2)/((√5 )^2 - √5 • √2) = (√3(√5 - √(2)))/(√5(√5 - √2)) = √3/√5 = (√3 • √5)/((√5 )^2 ) = √15/5; 10) (13 - √13)/√13 = ((√13 )^2 - √13)/√13 = (√13(√13- 1))/√13 = √13 – 1; 11) (a+2√ab+ b)/(√a+ √b) = ((√a )^2 + 2√ab + (√b )^2)/(√a + √b) = ((√a + √b )^2)/((√a + √b)) = √a + √b; 12) (4b^2 - 4b√c + c)/(2b - √c) = ((2b)^2 - 2 • 2b√c + (√c )^2)/(2b - √c) = ((2b- √c )^2)/((2b- √c)) = 2b – √c.