Question 595614
{{{y/(sqrt(7)+sqrt(3))}}}
Rationalizing two-term denominators makes use of the following pattern:
{{{(a+b)(a-b) = a^2 - b^2}}}
This pattern shows us how to take a two-term expression, an a+b or a-b, multiply it by something and get an expression made up of all perfect squares, {{{a^2-b^2}}}. Since your two-term denominator has a "+" between the terms it will play the role of a+b. So we need to multiply it (and the numerator) by a-b:
{{{(y/(sqrt(7)+sqrt(3)))((sqrt(7)-sqrt(3))/(sqrt(7)-sqrt(3)))}}}<br>
We already know that the denominator will be {{{a^2-b^2}}}. On top we just distribute the y:
{{{(y*sqrt(7)-y*sqrt(3))/((sqrt(7))^2-(sqrt(3))^2)}}}
which simplifies as follows:
{{{(y*sqrt(7)-y*sqrt(3))/(7-3)}}}
{{{(y*sqrt(7)-y*sqrt(3))/4}}}