Simplify ( square root of x-1)/(x-1)

Problem

√(,x−1)/(x−1)

Solution

1. Identify the expression as a fraction where the numerator is a square root and the denominator is the same expression raised to the power of 1.

2. Rewrite the square root in the numerator using a fractional exponent.

√(,x−1)=(x−1)(1/2)

3. Apply the quotient rule for exponents, which states that (am)/(an)=a(m−n)

((x−1)(1/2))/((x−1)1)=(x−1)(1/2−1)

4. Subtract the exponents to find the new power.

1/2−1=−1/2

5. Simplify the expression by moving the term with the negative exponent to the denominator.

(x−1)(−1/2)=1/((x−1)(1/2))

6. Convert the fractional exponent back into radical form.

1/((x−1)(1/2))=1/√(,x−1)

Final Answer

√(,x−1)/(x−1)=1/√(,x−1)

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