Question

Multiplying StartFraction 3 Over StartRoot 17 EndRoot minus StartRoot 2 EndRoot EndFraction by which fraction will produce an equivalent fraction with a rational denominator?

Answer 1

Answer:

B)

Step-by-step explanation:

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Answer 2

The fraction which produce an equivalent fraction with a rational denominator is $\left(\frac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}\right)$

Explanation:

The equation is $\frac{3}{\sqrt{17}-\sqrt{2}}$

To find the rational denominator, let us take conjugate of the denominator and multiply the conjugate with both numerator and denominator.

Rewriting the equation, we have,

$\frac{3}{\sqrt{17}-\sqrt{2}}\left(\frac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}\right)$

Multiplying, we get,

$\frac{3(\sqrt{17}+\sqrt{2})}{(\sqrt{17})^{2}-(\sqrt{2})^{2}}$

Simplifying the denominator, we get,

$\frac{3(\sqrt{17}+\sqrt{2})}{17-2}$

Subtracting, the values of denominator,

$\frac{3(\sqrt{17}+\sqrt{2})}{15}$

Dividing the numerator and denominator,

$\frac{\sqrt{17}+\sqrt{2}}{5}$

Hence, the denominator has become a rational denominator.

Thus, the fraction which produce an equivalent fraction with a rational denominator is $\left(\frac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}\right)$