Ответ(ы) на вопрос:
Гость 1)
14a⁴b / 49a³b² = 2a / 7b
3x /(x²+4x) = 3x / (x(x+4)) = 3 / (x+4)
(y²-z²) / (2y+2z) = ( (y-z)(y+z) ) / ( 2(y+z)) = (y-z)/2 = 0.5(y-z)
2)
a) (3x-1)/x² - (x-9)/3x = ( 3(3x-1) - x(x-9) ) / 3x² =
= (9x-3-x²+9x) /3x² = (-x²+18x-3) /3x² =
= - (x²-18x+3)/3x²
б) 1/(2а-b) - 1/(2a+b) = ((2a+b) - (2a-b)) / ((2a-b)(2a+b) )=
= (2a+b-2a+b) / ( (2a)² -b²) = 2b/(4a²-b²)
в) 5/(c+3) - (5c-2)/(c²+3c) = 5/(c+3) - (5c-2) / (c*(c+3))=
= (5c -5c+2)/ (c(c+3)) = 2/ (c(c+3)) = 2/ (c²+3c)
3)
(a²-b)/a - a = (a²-b -a²) /a = -b/a
при а=0,2 ; b=-5
- (-5) / 0.2 = - (-25) = 25
проверим на полном выражении:
( 0,2² - (-5)) /0,2 - 0,2 = (0,04+5)/0,2 -0,2 =
= 5,04/0,2 -0,2 = 25,2 -0,2 =25
4) 3/(х-3) - [(х+15) /(х²-9)] - 2/x=
= 3/(x-3) - [(x+15)/ (x-3)(x+3) ] - 2/x=
= (3x(x+3) - x(x+15) -2(x-3)(x+3) ) / (x(x-3)(x+3)) =
= (3x² + 9x - x² - 15x - 2x² +18 ) / (x(x-3)(x+3)) =
= ( (3x²-x²-2x²) + (9x-15x) +18 ) / (x(x-3)(x+3)) =
= (6x+18) / (x(x-3)(x+3)) = (6(x+3) ) / (x(x-3)(x+3)) =
= 6 / (x(x-3) ) = 6 / (x²-3x)
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