Розділ 1. РАЦІОНАЛЬНІ ВИРАЗИ » 7.2

7.2 Виконайте дії: 1) (10x+y)/5x – (3y^2)/x^2 • x/15y = (10x+y)/5x – (3y^2 • x)/(x^2 • 15y) = (10x+y)/5x – y/5x = (10x+y-y)/5x = 10x/5x = 2; 2) (a^2- 4)/(9- b^2 ) : (a-2)/(3+b) – 2/(3-b) = ((a-2)(a+2)(3+b))/((3-b)(3+b)(a-2)) – 2/(3-b) = (a+2)/(3-b) – 2/(3-b) = (a+2-2)/(3-b) = a/( 3-b); 3) (x+y)/(3x-y) + 1/(x+y) • (x^2- y^2)/(3x-y) = (x+y)/(3x-y) + (1 • (x-y)(x+y))/((x+y)(3x-y)) = (x+y)/(3x-y) + (x-y)/(3x-y) = (x+y+x-y)/(3x-y) = 2x/(3x-y); 4) m + (m^2+ mn)/(n-m) • m/(m+n) = m + m(m+n)m/((n-m)(m+n)) = m + m^2/(n-m) = (mn- m^2+ m^2)/(n-m) = mn/(n-m).