Вправи: 393

393. Спростіть вираз:

1) 1x + x^–1 = 1x + 1x = 1+1x = 2x; 2) 2a + a^–1 = 2a + 1a = 2+1a = 3a;

3) 3m2 + m^–2 = 3m2 + 1m2 = 3+1m2 = 4m2;

4) (x + 5)^–1 + 1x+5 = 1x+5 + 1x+5 = 2x+5;

5) (a + 2)^–1 – 2a+2 = 1a+2 – 2a+2 = –1a+2;

6) a(a + b)^–1 + b(a + b)^–1 = aa+ b + ba+ b = a+ ba+ b = 1;

7) (1 + b)⁰ – (1 + b)^–1 = 1\1+b – 11+ b = 1+ b-11+ b = b1+ b;

8) (a + b)^–1 + (a + b)⁰ = 1a+ b + 1\a+b = 1+ a+ ba+ b;

9) (x – 2)^–1 – x(2 – x)^–1 = 1x-2 – x2- x = 1x-2 + xx-2 = 1+ xx-2;

10) (5 – b)^–1 + (5 – b)^–1 = 1\5-b5+ b + 1\5+b5-b = 5- b+5+ b(5+ b)(5- b) = 1025- b2.