Question

Упростить дробнр-рациональное выражение: √38.8, даю 50 баллов.

Answer 1

$1)\ \ \dfrac{18a-3a^2}{8a^2-48a}=\dfrac{-3a(a-6)}{8a(a-6)}=-\dfrac{3}{8}\\\\\\2)\ \ \dfrac{8p-40}{15-3p}=\dfrac{8(p-5)}{-3(p-5)}=-\dfrac{8}{3}=-2\dfrac{2}{3}\\\\\\4)\ \ \dfrac{(3x+6y)^2}{5x+10y}=\dfrac{(3\cdot (x+2y))^2}{5\cdot (x+2y)}=\dfrac{9\cdot (x+2y)^2}{5\cdot (x+2y)}=\dfrac{9(x+2y)}{5}\\\\\\5)\ \ \dfrac{ax+bx-ay-by}{bx-by}=\dfrac{(a+b)\, x-(a+b)\, y}{b(x-y)}=\dfrac{(a+b)(x-y)}{b(x-y)}=\dfrac{a+b}{b}\\\\\\7)\ \ \dfrac{(2a-2b)^2}{a-b}=\dfrac{\Big(2(a-b)\Big)^2}{a-b}=\dfrac{4\, (a-b)^2}{a-b}=4\, (a-b)$

$8)\ \ \dfrac{(4c+12d)^2}{c+3d}=\dfrac{\Big(4\, (c+3d)\Big)^2}{c+3d}=\dfrac{16(c+3d)^2}{c+3d}=16\, (c+3d)\\\\\\10)\ \ \dfrac{ab-3b-2a+6}{15-5a}=\dfrac{b\, (a-3)-2\, (a-3)}{-5\, (a-3)}=\dfrac{(a-3)(b-2)}{-6(a-3)}=\dfrac{b-2}{-6}=\dfrac{2-b}{6}$