Bài 4: Quy đồng mẫu thức nhiều phân thức

\(a,\dfrac{2x-1}{x+1}=\dfrac{5\left(2x-1\right)}{5\left(x+1\right)}=\dfrac{10x-5}{5\left(x+1\right)}\\ \dfrac{-4x}{5+5x}=\dfrac{-4x}{5\left(x+1\right)}\)

\(b,\dfrac{-7}{3x-2}=\dfrac{-7.2\left(3x+2\right)}{2\left(3x+2\right)\left(3x-2\right)}=\dfrac{-14\left(3x+2\right)}{2\left(3x+2\right)\left(3x-2\right)}\\ \dfrac{1+x}{6x+4}=\dfrac{1+x}{2\left(3x+2\right)}=\dfrac{\left(3x-2\right)\left(1+2x\right)}{2\left(3x+2\right)\left(3x-2\right)}\)

Lời giải:

\(\dfrac{3x}{x^2-2}=\dfrac{3x.x.\left(x+2\right)}{\left(x^2-2\right).x.\left(x+2\right)}=\dfrac{3x^2\left(x+2\right)}{x\left(x+2\right)\left(x^2-2\right)}\)

\(\dfrac{x-1}{x^2+2x}=\dfrac{x-1}{x\left(x+2\right)}=\dfrac{\left(x-1\right)\left(x^2-2\right)}{x\left(x+2\right)\left(x^2-2\right)}\)

\(\dfrac{x-1}{x^2+5x}=\dfrac{\left(x-1\right)\left(x-5\right)}{x\left(x-5\right)\left(x+5\right)};\dfrac{x+1}{x^2-25}=\dfrac{x\left(x+1\right)}{x\left(x-5\right)\left(x+5\right)}\)

quy đồng mẫu số hộ mình

\(\dfrac{x}{4x-16}=\dfrac{x}{4\left(x-4\right)}=\dfrac{-5x}{20\left(4-x\right)}\)

\(\dfrac{1+x}{20-5x}=\dfrac{1+x}{5\left(4-x\right)}=\dfrac{4+4x}{20\left(4-x\right)}\)

\(\dfrac{x}{4x-16}=\dfrac{x}{4\left(x-4\right)}=\dfrac{5x}{20\left(x-4\right)}\\ \dfrac{1+x}{20-5x}=\dfrac{-\left(x+1\right)}{5\left(x-4\right)}=\dfrac{-4\left(x+1\right)}{20\left(x-4\right)}\)

\(9,\dfrac{2}{x^2-2x}=\dfrac{6}{3x\left(x-2\right)};\dfrac{x}{3x-6}=\dfrac{x^2}{3x\left(x-2\right)}\\ 10,\dfrac{x}{x-5}=\dfrac{x}{x-5};x+1=\dfrac{\left(x+1\right)\left(x-5\right)}{x-5}\\ 11,-3=\dfrac{-3\left(x^2+x+5\right)}{x^2+x+5}\\ 12,\dfrac{x}{2x-8}=\dfrac{x^2}{2x\left(x-4\right)};\dfrac{x+1}{4x-x^2}=\dfrac{-2\left(x+1\right)}{2x\left(x-4\right)}\)

\(\left\{{}\begin{matrix}\dfrac{3x+1}{6xy^4}\\\dfrac{x^2-5}{4x^2y^3}\end{matrix}\right.\)

⇒ \(\left\{{}\begin{matrix}\dfrac{2x\left(3x+1\right)}{12x^2y^4}\\\dfrac{3y\left(x^2-5\right)}{12x^2y^4}\end{matrix}\right.\)