Select the answer which is equivalent to the given expression using your calculator. (-6)/(-17-sqrt7) (34+2sqrt7)/(47) (34-2sqrt7)/(47) (17+sqrt7)/(47) (17-sqrt7)/(47)

Question

Select the answer which is equivalent to the given expression using your calculator.  (-6)/(-17-sqrt7)  (34+2sqrt7)/(47)  (34-2sqrt7)/(47)  (17+sqrt7)/(47)  (17-sqrt7)/(47)

Bytelearn · Accepted Answer

Rationalize Denominator: First, we need to rationalize the denominator of the given expression (-6)/(-17-sqrt7) because it contains a square root. To do this, we will multiply both the numerator and the denominator by the conjugate of the denominator, which is (-17+sqrt7).Multiply by Conjugate: The conjugate of (-17-sqrt7) is (-17+sqrt7). We multiply the numerator and the denominator by this conjugate to rationalize the denominator: ((-6)/(-17-sqrt7)) * ((-17+sqrt7)/(-17+sqrt7))Perform Multiplication: Now, we perform the multiplication in the numerator and the denominator separately: Numerator: -6 * (-17+sqrt7) = 102 - 6sqrt7 Denominator: (-17-sqrt7) * (-17+sqrt7) = (-17)^2 - (sqrt7)^2 = 289 - 7 = 282Simplify Expression: Now we have the expression in the form: (102 - 6sqrt7) / 282Divide by Greatest Common Divisor: We can simplify this expression by dividing both the terms in the numerator by the denominator: 102/282 - (6sqrt7)/282Combine Terms: Simplify the fractions by dividing the numerator and the denominator by their greatest common divisor, which is 6 for both terms: (102/6) / (282/6) - (6/6)sqrt7 / (282/6) 17/47 - sqrt7 / 47Combine the terms to get the final simplified expression: (17 - sqrt7) / 47

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\frac{-6}{-17-\sqrt{7}}$ $\newline$ $\frac{34+2 \sqrt{7}}{47}$ $\newline$ $\frac{34-2 \sqrt{7}}{47}$ $\newline$ $\frac{17+\sqrt{7}}{47}$ $\newline$ $\frac{17-\sqrt{7}}{47}$

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