Rationalize the Numerator and Simplify $\frac { 5 + \sqrt { 2 } } { 5 - \sqrt { 2 } }$

question 33

Multiple Choice

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
- $\frac { 5 + \sqrt { 2 } } { 5 - \sqrt { 2 } }$

• A) \(\frac { 27 } { 23 - 10 \sqrt { 2 } }\)
• B) 1
• C) \(\frac { 23 } { 27 - 10 \sqrt { 2 } }\)
• D) \(\frac { 23 } { 27 + 10 \sqrt { 2 } }\)

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Definitions:

Regressive Tax

A tax imposed in such a manner that the tax rate decreases as the amount subject to taxation increases.

Proportional Tax

A tax system where the tax rate remains constant regardless of the amount subject to tax, meaning everyone pays the same percentage of their income.

Progressive Tax

A tax system where the tax rate increases as the taxable amount increases, burdening wealthier individuals more.

Progressive Tax

A tax system in which tax rates increase as the taxable amount increases, placing a higher tax burden on individuals with higher incomes.