\(a)\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1}\left(x\ne1\right)\\ \Leftrightarrow\dfrac{4x-5}{x-1}-\dfrac{x}{x-1}=2\\ \Leftrightarrow\dfrac{3x-5}{x-1}=2\\ \Leftrightarrow3x-5=2\left(x-1\right)\\ \Leftrightarrow3x-5=2x-2\\ \Leftrightarrow x=-2+5\\ \Leftrightarrow x=3\left(tm\right)\)
\(b)\dfrac{7}{x+2}=\dfrac{3}{x-5}\left(x\ne-2;x\ne5\right)\\ \Leftrightarrow7\left(x-5\right)=3\left(x+2\right)\\\Leftrightarrow7x-35=3x+6\\ \Leftrightarrow 7x-3x=6+35\\ \Leftrightarrow4x=41\\ \Leftrightarrow x=\dfrac{41}{4}\left(tm\right)\)
c)
\(\dfrac{2x+5}{2x}-\dfrac{x}{x+5}=0\left(x\ne-5;x\ne0\right)\\ \Leftrightarrow\dfrac{2x+5}{2x}=\dfrac{x}{x+5}\\ \Leftrightarrow\left(2x+5\right)\left(x+5\right)=2x\cdot x\\ \Leftrightarrow2x^2+10x+5x+25=2x^2\\ \Leftrightarrow15x+25=0\\ \Leftrightarrow x=\dfrac{-25}{15}\\ \Leftrightarrow x=\dfrac{-5}{3}\left(tm\right)\)
a, đk x khác 1
\(\Rightarrow4x-5=2x-2+x\Leftrightarrow x=3\)(tm)
b, đk x khác -2 ; 5
\(\Rightarrow7\left(x-5\right)=3\left(x+2\right)\Leftrightarrow7x-35=3x+6\Leftrightarrow4x=41\Leftrightarrow x=\dfrac{41}{4}\left(tm\right)\)
c, đk x khác 0 ; -5
\(\Rightarrow\left(2x+5\right)\left(x+5\right)-2x^2=0\Leftrightarrow2x^2+15x+25-2x^2=0\Leftrightarrow15x+25=0\Leftrightarrow x=-\dfrac{5}{3}\)
d, x khác 2 / 3 ; 4
\(\Rightarrow6.14\left(x-4\right)-6\left(3x-2\right)\left(x+2\right)=-9\left(3x-2\right)-5\left(3x-2\right)\left(x-4\right)\)
\(\Leftrightarrow84\left(x-4\right)-6\left(3x^2+4x-4\right)=-27x+18-5\left(3x^2-14x+8\right)\)
\(\Leftrightarrow84x-336-18x^2-24x+24=-27x+18-15x^2+70x-40\)
\(\Leftrightarrow3x^2+3x+290=0\Leftrightarrow3\left(x^2+x+1-1\right)+290=0\Leftrightarrow3\left(x^2+x+1\right)+287=0\)
vô lí
do x^2 + x + 1 > 0
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