Simplify each expression (5)/(1-sqrt7)

Identify Conjugate of Denominator: Identify the conjugate of the denominator. The conjugate of (1 - sqrt(7)) is (1 + sqrt(7)). We will multiply the numerator and the denominator by this conjugate to rationalize the denominator.Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate. (5)/(1 - sqrt(7)) * (1 + sqrt(7))/(1 + sqrt(7)) = (5 * (1 + sqrt(7)))/((1 - sqrt(7)) * (1 + sqrt(7)))Apply Difference of Squares: Apply the difference of squares to the denominator. (1 - sqrt(7)) * (1 + sqrt(7)) = 1^2 - (sqrt(7))^2 = 1 - 7 = -6Distribute Numerator: Distribute the numerator. 5 * (1 + sqrt(7)) = 5 + 5 * sqrt(7)Combine Results: Combine the results from Step 3 and Step 4. (5 + 5 * sqrt(7))/(-6)Simplify Expression: Simplify the expression by dividing each term in the numerator by the denominator. (5/-6) + (5 * sqrt(7)/-6) = -5/6 - (5 * sqrt(7))/6

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Simplify each expression. $\newline$ $\frac{5}{1-\sqrt{7}}$

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Q. Simplify each expression.

\newline

\frac{5}{1-\sqrt{7}}

Identify Conjugate of Denominator: Identify the conjugate of the denominator. $\newline$ The conjugate of $(1 - \sqrt{7})$ is $(1 + \sqrt{7})$ . We will multiply the numerator and the denominator by this conjugate to rationalize the denominator.
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate. $(\frac{5}{1 - \sqrt{7}}) \cdot \frac{1 + \sqrt{7}}{1 + \sqrt{7}} = \frac{5 \cdot (1 + \sqrt{7})}{(1 - \sqrt{7}) \cdot (1 + \sqrt{7})}$
Apply Difference of Squares: Apply the difference of squares to the denominator. $\newline$ $(1 - \sqrt{7}) * (1 + \sqrt{7}) = 1^2 - (\sqrt{7})^2 = 1 - 7 = -6$
Distribute Numerator: Distribute the numerator. $\newline$ $5 \times (1 + \sqrt{7}) = 5 + 5 \times \sqrt{7}$
Combine Results: Combine the results from Step $3$ and Step $4$ . $\newline$ $(5 + 5 \times \sqrt{7})/(-6)$
Simplify Expression: Simplify the expression by dividing each term in the numerator by the denominator. $\newline$ $(\frac{5}{-6}) + (\frac{5 \cdot \sqrt{7}}{-6}) = -\frac{5}{6} - (\frac{5 \cdot \sqrt{7}}{6})$