a) \(7x-2=5x+3\)
\(\Leftrightarrow7x-5x=3+2\)
\(\Leftrightarrow2x=5\)
\(\Leftrightarrow x=\dfrac{5}{2}\)
b) \(2\left(y-3\right)=3\left(y+1\right)\)
\(\Leftrightarrow2y-6=3y+3\)
\(\Leftrightarrow3y-2y=-6-3\)
\(\Leftrightarrow y=-9\)
c) \(x\left(x+1\right)-\left(x+2\right)\left(x-3\right)=7\)
\(\Leftrightarrow x^2+x-\left(x^2-x-6\right)=7\)
\(\Leftrightarrow x^2+x-x^2+x=7-6\)
\(\Leftrightarrow2x=1\)
\(\Leftrightarrow x=\dfrac{1}{2}\)
e) \(\dfrac{x+2}{x-2}-\dfrac{x-2}{x+2}=\dfrac{1}{x^2-4}\) (ĐKXĐ: \(x\ne\pm2\))
\(\Leftrightarrow\dfrac{\left(x+2\right)^2}{\left(x-2\right)\left(x+2\right)}-\dfrac{\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}=\dfrac{1}{\left(x-2\right)\left(x+2\right)}\)
\(\Rightarrow x^2+4x+4-\left(x^2-4x+4\right)=1\)
\(\Leftrightarrow8x=1\)
\(\Leftrightarrow x=\dfrac{1}{8}\) (thỏa mãn ĐKXĐ)
d) \(\dfrac{x}{x-1}+\dfrac{x-1}{x}=2\) (ĐKXĐ: \(x\ne0;x\ne1\))
\(\Leftrightarrow\dfrac{x^2}{x\left(x-1\right)}+\dfrac{\left(x-1\right)^2}{x\left(x-1\right)}=\dfrac{2x\left(x-1\right)}{x\left(x-1\right)}\)
\(\Rightarrow x^2+x^2-2x+1=2x^2-2x\)
\(\Leftrightarrow2x^2-2x+1=2x^2-2x\)
\(\Leftrightarrow1=0\) (vô lí)
\(\Rightarrow\) Pt đã cho vô nghiệm
f) \(\dfrac{x+3}{x}=\dfrac{2x+1}{2x-4}\) (ĐKXĐ: \(x\ne0;x\ne2\))
\(\Rightarrow\left(x+3\right)\left(2x-4\right)=\left(2x+1\right)x\)
\(\Leftrightarrow2x^2+2x-12=2x^2+x\)
\(\Leftrightarrow2x-x=12\)
\(\Leftrightarrow x=12\) (thỏa mãn ĐKXĐ)
$\text{#}Toru$
