Вправи 101 - 200 » 143

143. Спростіть вираз: 1) (a-b)/7a : (a-b)/7b = ((a-b) • 7b)/(7a • (a-b)) = b/a; 2) (x^2- y^2)/x^2 : (6x+6y)/x^5 = ((x-y)(x+y) • x^5)/(x^2 • 6 • (x+y)) = (x^3 (x-y))/6 = (x^4- x^3 y)/6; 3) (c-5)/(c^2- 4c) : (c-5)/(5c-20) = ((c-5) • 5(c-4))/(c(c-4)•(c-5)) = 5/c; 4) (x-y)/xy : (x^2- y^2)/3xy = ((x-y)•3xy)/(xy(x-y)(x+y)) = 3/(x+y); 5) (a^2- 25)/(a+7) : (a-5)/(a+7) = ((a-5)(a+5)(a+7))/((a+7)(a-5)) = (a+5)/1 = a + 5; 6) (a^2- 4a+4)/(a+2) : (a – 2) = ((a-2)^2 • 1)/((a+2)(a-2)) = (a-2)/(a+2); 7) ((p^2- 16k^2))/1 : (p+4k)/p = ((p-4k)(p+4k) • p)/(1 • (p+4k)) = p(p – 4k) = p2 – 4pk; 8) (a^2- ab)/a^2 : (a^2- 2ab+ b^2)/ab = a(a-b)ab/(a^2 (a-b)^2 ) = b/(a-b).