Rationalizing a Binomial Denominator Test

Question 1 of 5: Simplify

$$\frac{2\sqrt{2}}{3\sqrt{5}-5\sqrt{2}}$$

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$$\frac{-3\sqrt{5}-10}{15}$$

$$\frac{-2\sqrt{10}-5}{15}$$

$$\frac{-6\sqrt{5}-10}{5}$$

$$\frac{-6\sqrt{10}-20}{5}$$

$$\frac{2\sqrt{5}-10}{15}$$

Question 2 of 5: Simplify

$$\frac{2}{5+4\sqrt{5}}$$

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$$\frac{-10+8\sqrt{5}}{55}$$

$$\frac{-2+5\sqrt{5}}{11}$$

$$\frac{4\sqrt{10}}{11}$$

$$\frac{\sqrt{5}}{55}$$

$$\frac{-10+2\sqrt{10}}{5}$$

Question 3 of 5: Simplify

$$\frac{5+3\sqrt{3}}{6+3\sqrt{3}}$$

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Not Correct! Thinking Emoji

$$\frac{3+\sqrt{15}}{5}$$

$$180$$

$$\frac{1+\sqrt{3}}{3}$$

$$\frac{1+\sqrt{30}}{3}$$

$$\frac{-3+3\sqrt{3}}{2}$$

Question 4 of 5: Simplify

$$\frac{6}{-3 + 4\sqrt{7x}}$$

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Not Correct! Thinking Emoji

$$\frac{1-2x\sqrt{14x}}{1-x^3}$$

$$\frac{8x-\sqrt{6}}{4-x^2}$$

$$\frac{-18 - 24\sqrt{7x}}{9 - 112x}$$

$$\frac{3x\sqrt{11}- \sqrt{77}}{1-x^2}$$

$$\frac{84-x^2}{7-7x}$$

Question 5 of 5: Simplify

$$\frac{6x\sqrt{3}}{9\sqrt{x^{3}}- 5\sqrt{10x}}$$

Finish »

Select the Correct Answer Below: Correct! Cool Emoji

Not Correct! Thinking Emoji

$$\frac{12\sqrt{x}-3\sqrt{5}}{-5x}$$

$$3x + \sqrt{2}$$

$$\frac{15\sqrt{5x}-\sqrt{5}}{-3+5x}$$

$$\frac{54x\sqrt{3x}+ 30\sqrt{30x}}{81x^{2}- 250}$$

$$\frac{2\sqrt{5x}-2x\sqrt{15}}{-3x}$$

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