Rationalize the denominator and simplify.
-$\frac{7-\sqrt{2}}{7+\sqrt{2}}$
A) 1
B) $\frac{51-14 \sqrt{2}}{47}$
C) $\frac{51+14 \sqrt{2}}{47}$
D) $\frac{47-14 \sqrt{2}}{51}$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator: $(7-\sqrt{2})$. This gives $\frac{(7-\sqrt{2})^2}{(7+\sqrt{2})(7-\sqrt{2})}$. Simplifying, the denominator becomes $47$ and the numerator becomes $51 - 14\sqrt{2}$, resulting in $\frac{51-14\sqrt{2}}{47}$.

Rationalize the Denominator and Simplify 7−27+2\frac{7-\sqrt{2}}{7+\sqrt{2}}7+2​7−2​​ A) 1 B) 51−14247\frac{51-14 \sqrt{2}}{47}4751−142​​ C) 51+14247\frac{51+14 \sqrt{2}}{47}4751+142​​

Rationalize the Denominator and Simplify $\frac{7-\sqrt{2}}{7+\sqrt{2}}$ A) 1
B) $\frac{51-14 \sqrt{2}}{47}$ C) $\frac{51+14 \sqrt{2}}{47}$