a) \(\frac{2a^2-3a-2}{a^2-4}=2\)
\(\Rightarrow2a^2-3a-2=2\left(a^2-4\right)\)
\(\Rightarrow2a^2-3a-2=2a^2-4\)
\(\Rightarrow-3a-2=-4\)
\(\Rightarrow-3a=-2\Rightarrow a=\frac{2}{3}\)
b) \(\frac{3a-1}{3a+1}+\frac{a-3}{a+3}=2\)
\(\Rightarrow\frac{\left(3a-1\right)\left(a+3\right)+\left(3a+1\right)\left(a-3\right)}{\left(3a+1\right)\left(a+3\right)}=2\)
\(\Rightarrow\frac{6a^2-6}{3a^2+10a+3}=2\)
\(\Rightarrow6a^2-6=2\left(3a^2+10a+3\right)\)
\(\Rightarrow6a^2-6=6a^2+20a+6\)
\(\Rightarrow-6=20a+6\Rightarrow20a=-12\)
\(\Rightarrow a=\frac{-3}{5}\)
a, \(\frac{2a^2-3a-2}{a^2-4}=2\)
\(\Leftrightarrow\frac{a\left(2a+1\right)-2\left(2a+1\right)}{a^2-4}=2\)
\(\Leftrightarrow\frac{\left(a-2\right)\left(2a+1\right)}{a^2-2^2}=2\)
\(\Leftrightarrow\frac{\left(a-2\right)\left(2a+1\right)}{\left(a-2\right)\left(a+2\right)}=2\)
\(\Leftrightarrow\frac{2a+1}{a+2}=2\)
\(\Leftrightarrow2a+1=2\left(a+2\right)\Leftrightarrow2a+1=2a+4\Leftrightarrow2a+1-2a-4=0\)
\(\Leftrightarrow-3\ne0\)(voli)
b, \(\frac{3a-1}{3a+1}+\frac{a-3}{a+3}=2\)
\(\Leftrightarrow\frac{\left(3a-1\right)\left(a+3\right)}{\left(3a+1\right)\left(a+3\right)}+\frac{\left(a-3\right)\left(3a+1\right)}{\left(a+3\right)\left(3a+1\right)}=\frac{2\left(3a+1\right)\left(a+3\right)}{\left(3a+1\right)\left(a+3\right)}\)
\(\Leftrightarrow\left(3a-1\right)\left(a+3\right)+\left(a-3\right)\left(3a+1\right)=2\left(3a+1\right)\left(a+3\right)\)
\(\Leftrightarrow6a^2-6=6a^2+20a+6\)
\(\Leftrightarrow6a^2-6-6a^2-20a-6=0\)
\(\Leftrightarrow-12-20a=0\)
\(\Leftrightarrow20a=-12\)
\(\Leftrightarrow a=-\frac{3}{5}\)
