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\(\dfrac{x^2-4}{x^2+2x}=\dfrac{\left(x-2\right)\left(x+2\right)}{x\left(x+2\right)}=\dfrac{x-2}{x}=\dfrac{\left(x-2\right)^2}{x\left(x-2\right)}\)
\(\dfrac{x}{x-2}=\dfrac{x^2}{x\left(x-2\right)}\)
\(a.\) Ta có:
\(MTC:\) \(\left(x+1\right)\left(x+2\right)\)
Do đó
\(\frac{3x}{x+1}=\frac{3x\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}\)
\(\frac{x+4}{x+2}=\frac{\left(x+1\right)\left(x+4\right)}{\left(x+1\right)\left(x+2\right)}\)
\(b.\) Ta có:
\(x^2+x=x\left(x+1\right)\)
\(x^2-1=\left(x-1\right)\left(x+1\right)\)
nên \(MTC:\) \(x\left(x-1\right)\left(x+1\right)\)
Do đó:
\(\frac{5}{x^2+x}=\frac{5}{x\left(x+1\right)}=\frac{5\left(x-1\right)}{x\left(x-1\right)\left(x+1\right)}\)
\(\frac{6}{x^2-1}=\frac{6}{\left(x-1\right)\left(x+1\right)}=\frac{6x}{x\left(x-1\right)\left(x+1\right)}\)
\(c.\) Ta có:
\(x^2-5x+4=x^2-x-4x+4=x\left(x-1\right)-4\left(x-1\right)=\left(x-1\right)\left(x-4\right)\)
\(2x^2-8x=2x\left(x-4\right)\)
nên \(MTC:\) \(2x\left(x-1\right)\left(x-4\right)\)
Do đó:
\(\frac{4}{x^2-5x+4}=\frac{4}{\left(x-1\right)\left(x-4\right)}=\frac{8x}{2x\left(x-1\right)\left(x-4\right)}\)
\(\frac{x+1}{2x^2-8x}=\frac{x+1}{2x\left(x-4\right)}=\frac{\left(x-1\right)\left(x+1\right)}{2x\left(x-1\right)\left(x-4\right)}\)
Làm nốt d :P
\(\frac{x+3}{2x^2-15x-8};\frac{3}{x^2-8x}\)
Ta có : \(2x^2-15x-8=\left(2x+1\right)\left(x-8\right)\)
\(x^2-8x=x\left(x-8\right)\)
MTC : \(x\left(x-8\right)\left(2x+1\right)\)
\(\frac{x+3}{2x^2-15x-8}=\frac{x+3}{\left(2x+1\right)\left(x-8\right)}=\frac{x^2+3x}{x\left(x-8\right)\left(2x+1\right)}\)
\(\frac{3}{x^2-8x}=\frac{3}{x\left(x-8\right)}=\frac{6x+3}{x\left(x-8\right)\left(2x+1\right)}\)
\(\frac{4}{x+2}\)và \(\frac{2-x}{x^2+4x+4}\)
Ta có : \(x^2+4x+4=\left(x+2\right)^2\)
\(\Rightarrow\text{MTC}=\left(x+2\right)^2\)
\(\Rightarrow\hept{\begin{cases}\frac{4}{x+2}=\frac{4\left(x+2\right)}{\left(x+2\right)\left(x+2\right)}=\frac{4x+8}{\left(x+2\right)^2}\\\frac{2-x}{x^2+4x+4}=\frac{2-x}{\left(x+2\right)^2}\end{cases}}\)
\(\dfrac{4}{x^2-3x+2}\) và \(\dfrac{1}{x^2-x}\)
\(\dfrac{4}{x^2-3x+2}=\dfrac{4}{\left(x-1\right)\left(x-2\right)}\)
\(\dfrac{1}{x^2-x}=\dfrac{1}{x\left(x-1\right)}\)
`MSC: x(x-1)(x-2)`
\(\dfrac{4}{\left(x-1\right)\left(x-2\right)}=\dfrac{4\cdot x}{x\left(x-1\right)\left(x-2\right)}=\dfrac{4x}{x\left(x-1\right)\left(x-2\right)}\)
\(\dfrac{1}{x\left(x-1\right)}=\dfrac{1\cdot\left(x-2\right)}{x\left(x-1\right)\left(x-2\right)}=\dfrac{x-2}{x\left(x-1\right)\left(x-2\right)}\)