46. Найдите значение дроби, предварительно сократив её: 1) (15a² + 10ab)/(3ab + 2b²), если a = −2, b = 0,4; 2) (9b² − 4c²)/(12b²c − 8bc²), если b = 1/3, c = −6; 3) (36x² − 12xy + y²)/(y² − 36x²), если x = 1,2, y = −3; 4) (a⁸ − a⁶)/(a⁹ + a⁸), если a = −0,1.

1) \(\dfrac{15a^2+10ab}{3ab+2b^2}=\dfrac{5a(a+2b)}{b(3a+2b)}\). При \(a=-2\), \(b=0.4\): \(\dfrac{12}{-2.08}=-\dfrac{75}{13}\).

2) \(\dfrac{9b^2-4c^2}{12b^2c-8bc^2}=\dfrac{(3b-2c)(3b+2c)}{4bc(3b-2c)}=\dfrac{3b+2c}{4bc}\). При \(b=\dfrac13\), \(c=-6\): \(\dfrac{-11}{-8}=\dfrac{11}{8}\).

3) \(\dfrac{(6x-y)^2}{(y-6x)(y+6x)}=-\dfrac{6x-y}{6x+y}\). При \(x=1.2\), \(y=-3\): \(-\dfrac{10.2}{4.2}=-\dfrac{17}{7}\).

4) \(\dfrac{a^6(a-1)(a+1)}{a^8(a+1)}=\dfrac{a-1}{a^2}\). При \(a=-0.1\): \(\dfrac{-1.1}{0.01}=-110\).

Ответ: 1) \(-\dfrac{75}{13}\); 2) \(\dfrac{11}{8}\); 3) \(-\dfrac{17}{7}\); 4) \(-110\).