Can someone please help me with these 7 questions please?

The solution to each of the question takes different approach, as the questions are taken from different concepts; however, a common operation among all questions, is factorization.

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Rewrite as:

Apply law of indices

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Apply negative power rule of indices

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Evaluate like terms

Factor out x^2

Factor out -2

Divide by y

Split

Rationalize

Rationalize

Apply difference of two squares to the denominator

Simplify

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Split

Evaluate all roots

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Factorize each

Factor out (r+3) in the numerator and (r + 6) in the denominator

Cancel out r - 2

Cancel out x

Expand the numerator of the 2nd fraction

Factorize

Factor out x - 7

Factor out 4 from 4x + 8

Cancel out x + 2

Factorize

Cancel out 3x

Take LCM

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Rewrite as:

Express as multiplication

Express y^2 - 9 as y^2 - 3^2

Express as difference of two squares

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