Problem 62

Question

Simplify each complex rational expression. $$\frac{8+\frac{1}{x}}{4-\frac{1}{x}}$$

Step-by-Step Solution

Verified
Answer
The simplified form of the given complex rational expression is \(\frac{8x+1}{4x-1}\)
1Step 1: Determine LCD and rewrite the expression
The least common denominator (LCD) in the equation is \(x\). Rewrite the expression to achieve a simplified denominator on both fractions by multiplying each part of the expression by the LCD. This gives: \(x * \frac{8+\frac{1}{x}}{4-\frac{1}{x}} = \frac{8x+1}{4x-1}\)
2Step 2: Simplify the result
The fraction generated from Step 1 doesn’t simplify any further. So the final answer will be \(\frac{8x+1}{4x-1}\).