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Chapter 0: Problem 74

Contain fractional expressions that occur frequently in calculus. Simplify each expression. $$\frac{\sqrt{x}-\frac{1}{4 \sqrt{x}}}{\sqrt{x}}$$

Short Answer

Expert verified
The simplified expression is \( \frac{3}{4} \)

Step by step solution

01

Simplify Fractions

Separate the division term into two parts. The expression becomes \( \sqrt{x} \div \sqrt{x} - \frac{1}{4 \sqrt{x}} \div \sqrt{x}\)
02

Fraction division rule

Apply the division rule for fraction \( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \). This gives us the following: \( 1 - \frac{1}{4}\)
03

Evaluate subtraction

Subtract the fraction from 1 to simplify the expression further, rendering: \( 1 - \frac{1}{4} = \frac{3}{4}\)

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