Solve frac{3sqrt{2}}{sqrt{128}-5sqrt{2}}=

$$\frac { 3 \sqrt { 2 } } { \sqrt { 128 } - 5 \sqrt { 2 } } =$$

Evaluate

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Solution Steps

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$\frac{3\sqrt{2}}{8\sqrt{2}-5\sqrt{2}}$$

Combine 8\sqrt{2} and -5\sqrt{2} to get 3\sqrt{2}.

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

Cancel out 3\sqrt{2} in both numerator and denominator.

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Factor

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