What would be the value of $a$ and $b$ in following rational expression? If $(5 + 2\sqrt{3})/(7 + \sqrt{3}) = (a - \sqrt{3b})$,
How do I find the value of $a$ and $b$ where $a$ and $b$ are rational numbers?

$$(5 + 2\sqrt{3}) = (7 + \sqrt{3})(a - \sqrt{3b})$$
                  $$=7a-7\sqrt b\sqrt 3 +a\sqrt 3-3\sqrt b$$
compare the coefficients of $\sqrt 3$ of both sides
we get$$7a-3\sqrt b=5$$ and   $$a-7\sqrt b=2$$
solve for a and b
$a=29/46$ and $\sqrt b=-9/46$  
