1.
a, \(\dfrac{18ab}{27bc}=\dfrac{18ab:9b}{27bc:9b}=\dfrac{2a}{3c}\)
b, \(\dfrac{-21b^2y^2}{-28by}=\dfrac{-21b^2y^2:\left(-7\right)by}{-28by:\left(-7\right)by}=\dfrac{3by}{4}\)
c, \(\dfrac{-49a^3}{14b^3}=\dfrac{-49a^3:7}{14b^3:7}=\dfrac{-7a^3}{2b^3}\)
d, \(\dfrac{12x^3y^2}{18xy^5}=\dfrac{6xy^2\cdot2x^2}{6xy^2\cdot3y^3}=\dfrac{2x^2}{3y^3}\)
2.
a,\(\dfrac{a^3\cdot\left(a-5\right)}{a-5}=\dfrac{a^3}{1}=a^3\)
b,\(\dfrac{3\cdot\left(b+7\right)^4}{8\cdot\left(b+7\right)^6}=\dfrac{3}{8\cdot\left(b+7\right)^2}\)
c,\(\dfrac{15x\cdot\left(x+5\right)^2}{20x^2\cdot\left(x+5\right)}=\dfrac{3\cdot\left(x+5\right)}{4x}\)
d,\(\dfrac{x^3-4x^2}{y\cdot\left(x-4\right)}=\dfrac{x^2}{y}\)
e,\(\dfrac{5\cdot\left(a-2x\right)^2}{2a^2-4ac}=\dfrac{5\cdot\left(a-2x\right)}{2a}\)
3.
a,\(\dfrac{ax-3a}{bx-3b}=\dfrac{a\cdot\left(x-3\right)}{b\cdot\left(x-3\right)}=\dfrac{a}{b}\)
b, \(\dfrac{5x+20y}{15x+60y}=\dfrac{5\cdot\left(x+4y\right)}{15\cdot\left(x+4y\right)}=\dfrac{5}{15}=\dfrac{1}{3}\)
c, \(\dfrac{3b-9c}{5b^2-15bc}=\dfrac{3\cdot\left(b-3c\right)}{5b\cdot\left(b-3c\right)}=\dfrac{3}{5b}\)
d, \(\dfrac{8a^2+40ab}{ab+5b^2}=\dfrac{8a\cdot\left(a+5b\right)}{b\cdot\left(a+5b\right)}=\dfrac{8a}{b}\)
4.
a,\(\dfrac{3x^2-12x+12}{x^4-8x}=\dfrac{3\cdot\left(x^2-4x+4\right)}{x\cdot\left(x^3-8\right)}=\dfrac{3\cdot\left(x-2\right)^2}{x\cdot\left(x-2\right)\cdot\left(x^2+2x+4\right)}=\dfrac{3\cdot\left(x-2\right)}{x\cdot\left(x^2+2x+4\right)}=\dfrac{3\cdot\left(x-2\right)}{x\cdot\left(x+2\right)^2}\)
b, \(\dfrac{7x^2+14x+7}{3x^2+3x}=\dfrac{7\cdot\left(x^2+2x+1\right)}{3x\cdot\left(x+1\right)}=\dfrac{7\cdot\left(x+1\right)^2}{3x\cdot\left(x+1\right)}=\dfrac{7\cdot\left(x+1\right)}{3x}\)
5.
a, \(\dfrac{45x\cdot\left(3-x\right)}{15x\cdot\left(x-3\right)^3}=\dfrac{3\cdot\left(3-x\right)}{\left(x-3\right)^3}=\dfrac{-3\cdot\left(x-3\right)}{\left(x-3\right)^3}=\dfrac{-3}{\left(x-3\right)^2}\)
b, \(\dfrac{36\cdot\left(x-2\right)^3}{36-16x}=\dfrac{36\cdot\left(x-2\right)^3}{16\cdot\left(2-x\right)}=\dfrac{36\cdot\left(-\left(x-2\right)\right)^3}{16\cdot\left(2-x\right)}=\dfrac{-36\cdot\left(2-x\right)^3}{16\cdot\left(2-x\right)}=\dfrac{-9\cdot\left(2-x\right)^2}{4}\)
c, \(\dfrac{x^2-xy}{5y^2-5xy}=\dfrac{x\cdot\left(x-y\right)}{5y\cdot\left(y-x\right)}=\dfrac{-x\cdot\left(y-x\right)}{5y\cdot\left(y-x\right)}=\dfrac{-x}{5y}\)
d, \(\dfrac{y^2-x^2}{x^3-3x^2y+3xy^2+y^3}=\dfrac{\left(x+y\right)\cdot\left(x-y\right)}{\left(x-y\right)^3}=\dfrac{-\left(x+y\right)\cdot\left(y-x\right)}{\left(x-y\right)^3}=\dfrac{-\left(x+y\right)}{\left(x-y\right)^2}\)
