Rationalize expression (5+2√6)/(7+4√3)

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The discussion focuses on rationalizing the expression \(\frac{5+2\sqrt{6}}{7+4\sqrt{3}}\) to express it in the form \(a-b\sqrt{3}\). Participants are guided to multiply both the numerator and denominator by the conjugate \(7-4\sqrt{3}\) to eliminate the square root in the denominator. This method is essential for simplifying expressions involving irrational numbers. The goal is to determine the values of \(a\) and \(b\) after performing the necessary algebraic operations.

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5+2 root 6 / 7+4root3 = a-b root3 find a and b
 
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Hello and welcome to MHB! (Wave)

I've moved this thread to our elementary algebra forum, since this is a better fit for the problem and I've give the thread a descriptive title. We are given:

$$\frac{5+2\sqrt{6}}{7+4\sqrt{3}}=a-b\sqrt{3}$$

And instructed to find $a$ and $b$. Do you have any work to show or thoughts on how to begin?
 
Start by "rationalizing the denominator". That is, multiply both numerator and denominator of [math]\frac{5+ 2\sqrt{6}}{7+ 4\sqrt{3}}[/math] by [math]7- 4\sqrt{3}[/math].
 

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