Rationalize the denominator. Assume all variables represent positive real numbers.
-$\frac{7-\sqrt{6}}{7+\sqrt{6}}$
A) $\frac{43-14 \sqrt{6}}{55}$
B) $\frac{55+14 \sqrt{6}}{43}$
C) 1
D) $\frac{55-14 \sqrt{6}}{43}$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator: $(7-\sqrt{6})(7-\sqrt{6})$ and $(7+\sqrt{6})(7-\sqrt{6})$. This results in $\frac{(7-\sqrt{6})^2}{49-6} = \frac{49 - 14\sqrt{6} + 6}{43} = \frac{55 - 14\sqrt{6}}{43}$.

Rationalize the Denominator 7−67+6\frac{7-\sqrt{6}}{7+\sqrt{6}}7+6​7−6​​ A) 43−14655\frac{43-14 \sqrt{6}}{55}5543−146​​ B) 55+14643\frac{55+14 \sqrt{6}}{43}4355+146​​ C) 1 D) 55−14643\frac{55-14 \sqrt{6}}{43}4355−146​​

Rationalize the Denominator $\frac{7-\sqrt{6}}{7+\sqrt{6}}$ A) $\frac{43-14 \sqrt{6}}{55}$ B) $\frac{55+14 \sqrt{6}}{43}$ C) 1
D) $\frac{55-14 \sqrt{6}}{43}$