Question

Помогите пожалуйста( Умножение и деление дробей.Возведение дроби в степень. Вариант А 1

Answer 1

1. а) 12x^3/25 * 5/(4x^4) = 12x^3/(4x^4) * 5/25 = 3/x * 1/5 = 3/(5x)

б) (2x-6) * x^2/(x-3) = 2(x-3) * x^2/(x-3) = 2x^2

в) (-3a/b^2)^2 = 9a^2/b^4

г) (y^2-y)/(2xy) * 2x/(y^2-1) = y(y-1)/[(y-1)(y+1)] * 2x/(2xy) = y/(y+1) * 1/y = 1/(y+1)

2. а) -4a/(5c^2) : [-a/(10c^4)] = 4a/(5c^2) * 10c^4/a = 4*10c^4/(5c^2) = 8c^2

б) (m^2-4n^2)/m^2 : (4m-8n) = [(m-2n)(m+2n)] / [4m^2*(m-2n)] = (m+2n)/(4m^2)

в) (2x-1)/(x^2-6x+9) : (1-2x)/(x^2-3x) = -(1-2x)/(x-3)^2 * x(x-3)/(1-2x) = -x/(x-3)

г) (2a-4)/(a^2+4) : (a^2-4a+4)/(a^4-16) = 2(a-2)/(a^2+4) * (a^2+4)(a^2-4)/(a-2)^2 =

= 2(a-2)(a-2)(a+2) / (a-2)^2 = 2(a+2)