If $a +b $,= 5 and $ab = 6$ . Find $\frac{1}{a}$ + $\frac{1}{b}$

Question

$a +b $ = 5 and $ab = 6$ . Find $\cfrac{1}{a}$ + $\cfrac{1}{b}$

Any Ideas on how to begin?

Many Thanks

Answer 1

$$\frac { 1 }{ a } +\frac { 1 }{ b } =\frac { a+b }{ ab } =\frac { 5 }{ 6 } $$

Answer 2

Since $a+b = 5$ and $ab = 6$, then $a,b$ can be the roots of polynomial $x^2-5x+6=0$

By fraction, $(x-2)(x-3) = 0$.

Out of symmetry, let $a = 2,b=3$, so $\frac{1}{a}+\frac{1}{b}= \frac{5}{6}$