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

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To rationalize the expression (5+2√6)/(7+4√3), the first step is to multiply both the numerator and denominator by the conjugate of the denominator, which is (7-4√3). This process eliminates the square root in the denominator, making it easier to express the fraction in the form a-b√3. After performing the multiplication and simplifying, the values of a and b can be determined. The discussion emphasizes the importance of starting with the rationalization technique to solve the problem effectively.
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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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