Вправи 101 - 200 » 169 (3-5)

3) (1/a + 2/b + a/b^2 ) • ab/(a^2- b^2 ) + 2/(b-a) = 1/b. 1. 1^(\b^2 )/a + 2^(\ab)/b + a^a/b^2 = (b^2+ 2ab+ a^2)/(ab^2 ) = ((a+b)^2)/(ab^2 ); 2. ((a+b)^2)/(ab^2 ) • ab/((a-b)(a+b)) = ((a+b) • ab)/(ab^2 (a-b)(a+b)) = (a+b)/(b(a-b)); 3. (a+b)/(b(a-b)) – 2^(\b)/(a-b) = (a+b-2b)/(b(a-b)) = (a-b)/(b(a-b)) = a/b; 4) (a/(a-1) – (a )/(a+1) – (a^2+ 1)/(1- a^2 )) : (a^2+ a)/((a-1)^2 ) = (a-1)/a. 1. a^(\a+1)/(a-1) – a^(\a-1)/(a+1) + (a^2+ 1)/((a-1)(1+a)) = (a(a+1)- a(a-1)+ a^2+ 1)/((a-1)(1+a)) = (a^2+ a- a^2+ a+ a^2+ 1)/((a-1)(1+a)) = (a^2+ 2a+1)/((a-1)(a+1)) = ((a+1)^2)/((a-1)(a+1)) = (a+1)/(a-1); 2. (a+1)/(a-1) : (a^2+ a)/((a-1)^2 ) = ((a+1(a-1)^2)/((a-1) • a(a+1)) = (a-1)/a; 5) ((x+2y^(\x+2y))/(x-2y) – (x-2y^(\x-2y))/(x+2y) – (16y^2)/(x^2- 4y^2 )) : 4y/(x+2y) = 2. 1. (x+2y^(\x+2y))/(x-2y) – (x-2y^(\x-2y))/(x+2y) – (16y^2)/(x^2- 4y^2 )=((x+2y)^2- (x-2y)^2- 16y^2)/((x-2y)(x+2y)) = (x^2+ 4xy+4y^2- x^2+ 4xy-4y^2- 16y^2)/(x^2- 4y^2 ) • (x+2y)/4y = (x^2+ 4xy+4y^2- (x^2- 4xy+4y^2 )- 16y^2)/((x-2y)(x+2y)) = (x^2+ 4xy+4y^2- x^2+ 4xy-4y^2- 16y^2)/((x-2y)(x+2y)) = (8xy-16y^2)/((x-2y)(x+2y)) = (8y(x-2y))/((x-2y)(x+2y)) = 8y/(x+2y); 2. 8y/(x+2y) : 4y/(x+2y) = (8y • (x+2y))/((x+2y) • 4y) = 2;