Quy đồng mẫu thức các phân thức :
a.\(\dfrac{-7y}{12xz^2}\);\(\dfrac{11z}{18x^2y}\)
b.\(\dfrac{3x+3}{12xy^3}\);\(\dfrac{x-2}{9x^2y}\)
c.\(\dfrac{1+2x}{2x+4}\);\(\dfrac{3-y}{x+2}\)
d.\(\dfrac{3x}{xy-y}\);\(\dfrac{y}{x-1}\)
e.\(\dfrac{1}{6x^3y^2}\);\(\dfrac{x+1}{x^2y^4}\);\(\dfrac{x-1}{4xz^3}\)
f.\(\dfrac{5}{4x}\);\(\dfrac{y}{2x-2}\);\(\dfrac{3+x}{8x^2-8x}\)
g.\(\dfrac{b}{2a}\);\(\dfrac{4a+3b^2}{18ab}\);\(\dfrac{x}{9b}\)
h.\(\dfrac{3+2x}{10x^4y}\);\(\dfrac{5}{8x^2y^2}\);\(\dfrac{2}{3xy^5}\)
i.\(\dfrac{x}{x-1}\);\(\dfrac{1}{x^2+2x+1}\)
j.\(\dfrac{1}{x^3-8}\);\(\dfrac{3}{2x-4}\)
k.\(\dfrac{x+3}{x^2-4}\);\(\dfrac{3}{2x+4}\)
l.\(\dfrac{x+2}{2x-4}\);\(\dfrac{4x}{x^2+4x+4}\)
a: \(\dfrac{-7y}{12xz^2}=\dfrac{-7y\cdot3\cdot x\cdot y}{12xz^2\cdot3xy}=\dfrac{-21xy^2}{36x^2yz^2}\)
\(\dfrac{11z}{18x^2y}=\dfrac{11z\cdot2\cdot z^2}{18x^2y\cdot2z^2}=\dfrac{22z^3}{36x^2yz^2}\)
b: \(\dfrac{3x+3}{12xy^3}=\dfrac{\left(3x+3\right)\cdot3\cdot x}{12xy^3\cdot3x}=\dfrac{9x^2+9x}{36x^2y^3};\dfrac{x-2}{9x^2y}=\dfrac{\left(x-2\right)\cdot4\cdot y^2}{9x^2y\cdot4y^2}=\dfrac{4xy^2-8y^2}{36x^2y^3}\)
c: \(\dfrac{2x+1}{2x+4}=\dfrac{2x+1}{2\left(x+2\right)};\dfrac{3-y}{x+2}=\dfrac{2\left(3-y\right)}{2\left(x+2\right)}=\dfrac{6-2y}{2\left(x+2\right)}\)
d: \(\dfrac{3x}{xy-y}=\dfrac{3x}{y\left(x-1\right)};\dfrac{y}{x-1}=\dfrac{y\cdot y}{y\left(x-1\right)}=\dfrac{y^2}{y\left(x-1\right)}\)
e: \(\dfrac{1}{6x^3y^2}=\dfrac{1\cdot y^2\cdot z^3}{6x^3y^2\cdot y^2z^3}=\dfrac{y^2z^3}{6x^3y^4z^3}\)
\(\dfrac{x+1}{x^2y^4}=\dfrac{\left(x+1\right)\cdot6\cdot x\cdot z^3}{x^2y^4\cdot6xz^3}=\dfrac{6xz^3\left(x+1\right)}{6x^3y^4z^3}\)
\(\dfrac{x-1}{4xz^3}=\dfrac{\left(x-1\right)\cdot1,5\cdot x^2\cdot y^4}{4xz^3\cdot1,5x^2y^4}=\dfrac{1,5x^2y^4\left(x-1\right)}{6x^3y^4z^3}\)
f: \(\dfrac{5}{4x}=\dfrac{5\cdot2\left(x-1\right)}{4x\cdot2\left(x-1\right)}=\dfrac{10x-10}{8x\left(x-1\right)}\)
\(\dfrac{y}{2x-2}=\dfrac{y}{2\left(x-1\right)}=\dfrac{y\cdot4x}{2\left(x-1\right)\cdot4x}=\dfrac{4xy}{8x\left(x-1\right)}\)
\(\dfrac{3+x}{8x^2-8x}=\dfrac{x+3}{8x\left(x-1\right)}\)
g: \(\dfrac{b}{2a}=\dfrac{b\cdot9\cdot b}{2a\cdot9b}=\dfrac{9b^2}{18ab}\)
\(\dfrac{4a+3b^2}{18ab}=\dfrac{4a+3b^2}{18ab}\)
\(\dfrac{x}{9b}=\dfrac{x\cdot2\cdot a}{9b\cdot2a}=\dfrac{2ax}{18ab}\)
h: \(\dfrac{2x+3}{10x^4y}=\dfrac{12y^4\left(2x+3\right)}{10x^4y\cdot12y^4}=\dfrac{12y^4\left(2x+3\right)}{120x^4y^5}\)
\(\dfrac{5}{8x^2y^2}=\dfrac{5\cdot15\cdot x^2y^3}{8x^2y^2\cdot15x^2y^3}=\dfrac{75x^2y^3}{120x^4y^5}\)
\(\dfrac{2}{3xy^5}=\dfrac{2\cdot40\cdot x^3}{3xy^5\cdot40x^3}=\dfrac{80x^3}{120x^4y^5}\)
i: \(\dfrac{x}{x-1}=\dfrac{x\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)^2}\)
\(\dfrac{1}{x^2+2x+1}=\dfrac{1}{\left(x+1\right)^2}=\dfrac{1\cdot\left(x-1\right)}{\left(x-1\right)\cdot\left(x+1\right)^2}=\dfrac{x-1}{\left(x-1\right)\left(x+1\right)^2}\)
j: \(\dfrac{1}{x^3-8}=\dfrac{1}{\left(x-2\right)\left(x^2+2x+4\right)}=\dfrac{1\cdot2}{2\left(x-2\right)\left(x^2+2x+4\right)}\)
\(=\dfrac{2}{\left(x-2\right)\left(x^2+2x+4\right)}\)
\(\dfrac{3}{2x-4}=\dfrac{3}{2\left(x-2\right)}=\dfrac{3\left(x^2+2x+4\right)}{2\left(x-2\right)\left(x^2+2x+4\right)}\)
k: \(\dfrac{x+3}{x^2-4}=\dfrac{x+3}{\left(x-2\right)\left(x+2\right)}=\dfrac{2\left(x+3\right)}{2\left(x-2\right)\left(x+2\right)}\)
\(\dfrac{3}{2x+4}=\dfrac{3}{2\left(x+2\right)}=\dfrac{3\cdot\left(x-2\right)}{2\left(x+2\right)\left(x-2\right)}=\dfrac{3x-6}{2\left(x+2\right)\left(x-2\right)}\)
l: \(\dfrac{x+2}{2x-4}=\dfrac{x+2}{2\left(x-2\right)}=\dfrac{\left(x+2\right)\cdot\left(x+2\right)^2}{2\left(x-2\right)\left(x+2\right)^2}=\dfrac{\left(x+2\right)^3}{2\left(x-2\right)\left(x+2\right)^2}\)
\(\dfrac{4x}{x^2+4x+4}=\dfrac{4x}{\left(x+2\right)^2}=\dfrac{4x\cdot2\cdot\left(x-2\right)}{2\left(x-2\right)\left(x+2\right)^2}=\dfrac{8x\left(x-2\right)}{2\left(x-2\right)\left(x+2\right)^2}\)
