help algebra

If

$a + b = 7$ and $a^3 + b^3 = 42 + ab$,

what is the value of the sum $\dfrac{1}{a} + \dfrac{1}{b}$?

$\begin{array}{|rcll|} \hline \left(a + b\right)^3 =&=& a^3+3a^2b+3ab^2+b^3 \\ \left(a + b\right)^3 =&=& a^3+b^3+3ab(a+b) \\ 7^3 =&=& 42+ab+3ab*7 \\ 343 =&=& 42+22ab \\ 22ab=&=& 343-42\\ ab &=& \dfrac{301}{22} \\ \hline \end{array}$

$\begin{array}{|rcll|} \hline \dfrac{1}{a} + \dfrac{1}{b} &=& \dfrac{a+b}{ab} \\\\ \dfrac{1}{a} + \dfrac{1}{b} &=& \dfrac{7}{\frac{301}{22}} \\\\ \dfrac{1}{a} + \dfrac{1}{b} &=& \dfrac{7*22}{301} \\\\ \dfrac{1}{a} + \dfrac{1}{b} &=& \dfrac{22}{43} \\ \hline \end{array}$