Question

Solve for $a:(a-2)+\frac{1}{a-2}=3;a\ne 2$

Answer 1

$(a-2)+\frac{1}{(a-2)}=3$

$(a-2{)}^2+1=3(a-2)$

$a^2-4a+4+1=3a-6$

$a^2-7a-11=0$

$a=\frac{7\pm \sqrt{49+4\times 11}}{2\times 1}$

$a=\frac{7\pm \sqrt{93}}{2}$

$a=\frac{7+\sqrt{93}}{2},a=\frac{7-\sqrt{93}}{2}$