Select the answer which is equivalent to the given expression using your calculator. (-13)/(-1-sqrt14) -7+7sqrt14 -1+sqrt14 -7-7sqrt14 -1-sqrt14

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Select the answer which is equivalent to the given expression using your calculator.  (-13)/(-1-sqrt14)  -7+7sqrt14  -1+sqrt14  -7-7sqrt14  -1-sqrt14

Bytelearn · Accepted Answer

Simplify Denominator: Simplify the denominator of the given expression. We have the expression (-13)/(-1-sqrt14). To simplify, we first look at the denominator, which is -1-sqrt14. We can rewrite this as -(1+sqrt14) to make it clearer that the entire expression is negative.Divide Numerator: Divide the numerator by the simplified denominator. Now we divide -13 by -(1+sqrt14). Since we have a negative divided by a negative, the result will be positive. So, the expression simplifies to 13/(1+sqrt14).Rationalize Denominator: Rationalize the denominator. To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of 1+sqrt14 is 1-sqrt14. So we multiply both the numerator and the denominator by 1-sqrt14.Perform Multiplication: Perform the multiplication. Multiplying the numerator: 13 * (1-sqrt14) = 13 - 13sqrt14. Multiplying the denominator: (1+sqrt14) * (1-sqrt14) = 1 - (sqrt14)^2.Evaluate Squares: Evaluate the squares and simplify the denominator. (sqrt14)^2 is simply 14. So the denominator becomes 1 - 14, which is -13.Simplify Entire Expression: Simplify the entire expression. Now we have (13 - 13sqrt14) / -13. Both terms in the numerator can be divided by -13, which gives us -1 + sqrt14.

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\frac{-13}{-1-\sqrt{14}}$ $\newline$ $-7+7 \sqrt{14}$ $\newline$ $-1+\sqrt{14}$ $\newline$ $-7-7 \sqrt{14}$ $\newline$ $-1-\sqrt{14}$

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