Вправи 501 - 595 » 536 (1-4)

Спростіть вираз: 1) a/(√a- 2) – (4√a- 4)/(√a- 2) = (a-(4√a- 4))/(√a- 2) = ((√a )^2- 2 • 2√a+ 2^2)/(√a- 2) = ((√a- 2)^2)/(√a- 2) = √a – 2; 2) (√m+ 1^(\√m))/(√m- 2) – (√m+ 3^(\√m- 2))/√m = ((√m )^2+ √m- ((√m )^2- 2√m+ 3√m- 6))/(√m(√m- 2)) = (m+ √m- m+2√m- 3√m+ 6)/(√m(√m- 2)) = 6/(√m(√m- 2)) = 6/(m-2√m); 3) (√y+ 4)/(√xy+ y) – (√x- 4)/(x+ √xy) = (√y+ 4)/(√xy+ (√y )^2 ) – (√x- 4)/((√x )^2+ √xy) = (√y+ 4^(\√x))/(√xy+ y) – (√x- 4^(\√y))/(x+ √xy) = (√xy+ 4√x- √xy+ 4√y)/(√xy(√x+ √y)) = (4(√x+ √(y)))/(√xy(√x+ √y)) = 4/√xy; 4) √a/(√a+ 4) – a/(a-16) = 〖√a〗^(\√a- 4)/(√a+ 4) – a/((√a+ 4)(√a- 4)) = ((√a )^2- 4√a- a)/((√a+ 4)(√a- 4)) = (a-4√a- a)/((√a+ 4)(√a- 4)) = –(4√a)/(a-16) = (4√a)/(16-a);