Simplify. Rationalize the denominator. 7/-3 + sqrt 2 ______

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Identify Conjugate of Denominator: Identify the conjugate of the denominator -3 + sqrt 2. The conjugate of a number of the form a + sqrt(b) is a - sqrt(b). Therefore, the conjugate of -3 + sqrt 2 is -3 - sqrt 2.Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the fraction by a form of 1 that will eliminate the square root in the denominator. This form of 1 is the conjugate of the denominator over itself. So, we multiply (7)/(-3 + sqrt 2) by (-3 - sqrt 2)/(-3 - sqrt 2).Apply Distributive Property: Apply the distributive property to the numerator. Multiply 7 by each term in the conjugate -3 - sqrt 2. 7 * (-3) = -21 7 * (-sqrt 2) = -7sqrt 2 So, the numerator becomes -21 - 7sqrt 2.Apply Difference of Squares: Apply the difference of squares formula to the denominator. The product of a binomial and its conjugate is the difference of squares: (-3 + sqrt 2) * (-3 - sqrt 2) = (-3)^2 - (sqrt 2)^2 9 - 2 = 7 So, the denominator becomes 7.Combine Numerator and Denominator: Combine the simplified numerator and denominator. The fraction is now (-21 - 7sqrt 2)/7.Simplify Fraction: Simplify the fraction by dividing each term in the numerator by the denominator. -21/7 = -3 -7sqrt 2/7 = -sqrt 2 So, the simplified expression is -3 - sqrt 2.

Simplify. Rationalize the denominator. $\newline$ $\frac{7}{-3 + \sqrt{2}}$

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Simplify. Rationalize the denominator. $\newline$ $\frac{7}{-3 + \sqrt{2}}$