Rewrite
[tex]\sec(A) - \tan(A) = \dfrac{(\sec(A) - \tan(A))(\sec(A) + \tan(A))}{\sec(A) + \tan(A)} = \dfrac{\sec^2(A) - \tan^2(A)}{\sec(A) + \tan(A)}[/tex]
Recall that
[tex]\cos^2(x) + \sin^2(x) = 1 \implies 1 + \tan^2(x) = \sec^2(x)[/tex]
which means
[tex]\sec^2(A) - \tan^2(A)[/tex]
and
[tex]\sec(A) - \tan(A) = \dfrac1{\sec(A) + \tan(A)}[/tex]
Then the value we want is simply the reciprocal of the given value,
[tex]\sec(A) + \tan(A) = \dfrac1{\sqrt3 - \sqrt2}[/tex]
and we can consider rationalizing the denominator to write
[tex]\dfrac1{\sqrt3 - \sqrt2} = \dfrac{\sqrt3 + \sqrt2}{\left(\sqrt3 - \sqrt2\right)\left(\sqrt3 + \sqrt2\right)} = \dfrac{\sqrt3 + \sqrt2}{\left(\sqrt3\right)^2 - \left(\sqrt2\right)^2} = \boxed{\sqrt3 + \sqrt2}[/tex]
