1) а)14a⁴b/49a³b² = 14/49 · a⁴⁻³ · 1/b¹⁻² = 14 ÷ 7/49 ÷ 7 · a¹1/d⁻¹ = 2/7 · ab¹ = 2ab/7
б)3x/(x² + 4x) = 3x/x(x + 4) = 3/1 · x¹⁻¹ · 1/(x + 4) = 3/1 · x⁰ · 1/(x + 4) = 3/1 · 1 · 1/(x + 4) = 3/(x + 4)
в)(y² - z²)/(2y + 2z) = (y - z)(y + z)/2(y + z) = (y - z)/2
2) а)(3x - 1)/x² + (x - 9)/3x = 3(3x - 1)/(3 · x²) + x(x - 9)/(3x · x) = (9x - 3)/3x² + (x² - 9x) /3x² = (9x - 3 + x² - 9x)/3x² = (x² - 3)/3x²
б)1/(2a - b) - 1/(2a + b) = (2a + b)/(2a - b)(2a + b ) - (2a - b)/(2a + b)(2a - b) =
=((2a + b) - (2a - b))/(2a + b)(2a - b) = (2a + b - 2a + b)/(4a² - b²) = b²/(4a² - b²)
в)5/(c + 3) - (5c - 2)/(c² + 3c) = 5/(c + 3) - (5c - 2)/c(c + 3) = 5c/c(c + 3) - (5c - 2)/ /c(c + 3) =(5c - 5c + 2)/c(c + 3) = 2/(c² +3 c)
3) (a² - b)/a - a/1 при a = 0,2; b = (-5)
((0,2) - (-5))/0,2 - 0,2 = (0,2 + 5)/0,2 - 0,2 = 5,2/0,2 - 0,2 = 5,2/0,2 -(0,2 · 0,2)/0,2 = = 5,2/0,2 - 0,04/0,2 = (5,2 - 0,04)/0,2 = 5,16/0,2 = 25,8 = 26
4) 3/(x -3) - (x + 15)/(x² - 9) - 2/x = 3/(x - 3) - (x + 15)/(x - 3)(x + 3) - 2/x = 3x(x + 3)/x(x- - 3)(x + 3) - x(x + 15)/x(x - 3)(x + 3) - 2(x - 3)(x + 3)/x(x - 3)(x + 3) = (3x(x + 3)) - x(x+ +15) - (2(x - 3)(x + 3))/x(x - 3)(x + 3) = (3x² + 9x - x² - 15x - 2(x² - 9))/x(x - 3)(x + 3) =
= (3x² + 9x - x² - 15x - 2x² + 18)/x(x - 3)(x + 3) = ((-6x) + 18)/x(x - 3)(x + 3) = (-6)(x + +3)/x(x - 3)(x + 3) = (-6)/(x² - 3x)