Question

Giải các phương trình:

\(a,\dfrac{3x-5}{x-2}=\dfrac{3x+1}{x-1}-\dfrac{3}{x-2}\)

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

Answer 1

a) \(\dfrac{3x-5}{x-2}=\dfrac{3x+1}{x-1}-\dfrac{3}{x-2}\left(ĐKXĐ:x\ne1;x\ne2\right)\)

\(\Leftrightarrow\dfrac{\left(3x-5\right)\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}=\dfrac{\left(3x+1\right)\left(x-2\right)}{\left(x-1\right)\left(x-2\right)}-\dfrac{3\left(x-1\right)}{\left(x-1\right)\left(x-2\right)}\)

\(\Rightarrow3x^2-3x-5x+5=3x^2-6x+x-2-3x+3\)

\(\Leftrightarrow3x^2-8x+5=3x^2-8x+1\)

\(\Leftrightarrow\left(3x^2-3x^2\right)-\left(8x-8x\right)=1-5\)

\(\Leftrightarrow0=-4\) (vô lí)

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