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Which of the following is equivalent to the given expression for all ?Choose answer:(A) (B) (C) D
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Q. Which of the following is equivalent to the given expression for all ?Choose answer:(A) (B) (C) D
- Simplify Square Roots: Simplify the square roots separately. can be simplified by taking the square root of and separately. The square root of is and the square root of is because . Similarly, can be simplified by taking the square root of and separately. The square root of is and the square root of is because .
- Divide Simplified Square Roots: Divide the simplified square roots.Now we have .We can cancel out the common terms from the numerator and the denominator.This leaves us with .
- Apply Quotient Rule: Apply the quotient rule for exponents. can be simplified by subtracting the exponents because . So, .
- Write Final Expression: Write the final simplified expression.The final simplified expression is .Now we need to match this with the given answer choices.
- Match with Answer Choices: Match the simplified expression with the answer choices.The expression matches with answer choice (B) .However, we need to ensure that the coefficient is correct.
- Check Coefficient: Check the coefficient.We initially simplified to and to , and these terms canceled each other out, leaving no coefficient.Therefore, the coefficient should be , not .This means there is a mistake in our previous steps.
