34. Найдите значение дроби: а) (15a² − 10ab)/(3ab − 2b²) при a = −2, b = −0,1; б) (9c² − 4d²)/(18c²d − 12cd²) при c = 2/3, d = 1/2; в) (6x² + 12xy)/(5xy + 10y²) при x = 2/3, y = −0,4; г) (x² + 6xy + 9y²)/(4x² + 12xy) при x = −0,2, y = −0,6.

1. \(\dfrac{15a^2-10ab}{3ab-2b^2}=\dfrac{5a(3a-2b)}{b(3a-2b)}=\dfrac{5a}{b}\).

   При \(a=-2\), \(b=-0.1\): \(\dfrac{5a}{b}=\dfrac{5\cdot(-2)}{-0.1}=100\).

2. \(\dfrac{9c^2-4d^2}{18c^2d-12cd^2}=\dfrac{(3c-2d)(3c+2d)}{6cd(3c-2d)}=\dfrac{3c+2d}{6cd}\).

   При \(c=\dfrac23\), \(d=\dfrac12\): \(\dfrac{3\cdot\frac23+2\cdot\frac12}{6\cdot\frac23\cdot\frac12}=\dfrac{3}{2}=1\).

3. \(\dfrac{6x^2+12xy}{5xy+10y^2}=\dfrac{6x(x+2y)}{5y(x+2y)}=\dfrac{6x}{5y}\).

   При \(x=\dfrac23\), \(y=-0.4\): \(\dfrac{6\cdot\frac23}{5\cdot(-0.4)}=\dfrac4{-2}=-2\).

4. \(\dfrac{x^2+6xy+9y^2}{4x^2+12xy}=\dfrac{(x+3y)^2}{4x(x+3y)}=\dfrac{x+3y}{4x}\).

   При \(x=-0.2\), \(y=-0.6\): \(\dfrac{-0.2+3\cdot(-0.6)}{4\cdot(-0.2)}=\dfrac{-2}{-0.8}=2.5\).

Ответ: а) 100; б) 1; в) −2; г) 2,5.