ГДЗ Алгебра 8 клас Істер (2025)

7.1 Виконайте дії:

1) (12a+b)/3a – (7b^2)/a^2 • a/21b = (12a+b)/3a – (7b^2 •a)/(a^2 •21b) = (12a+b)/3a – b/3a = (12a+b-b)/3a = 12a/3a = 4;
2) (m^2- n^2)/(x^2- 9) • (x-3)/(m-n) – m/(x+3) = ((m-n)(m+n)(x-3))/((x-3)(x+3)(m-n)) – m/(x+3) = (m+n)/(x+3) – m/(x+3) = (m+n-m)/(x+3) = n/(x+3);
3) (a-b)/(2a+b) + 1/(a-b) : (2a+b)/(a^2- b^2 ) = (a-b)/(2a+b) + (1 •(a-b)(a+b))/((a-b)(2a+b)) = (a-b)/(2a+b) + (a+b)/(2a+b) = (a-b+a+b)/(2a+b) = 2a/(2a+b);
4) x – (x^2- xy)/(x+y) • x/(x-y) = x – (x(x-y) •x)/((x+y)(x-y)) = x – x^2/(x+y) = (x^2+ xy- x^2)/(x+y) = xy/(x+y).