Problem 60

Question

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

Step-by-Step Solution

Verified
Answer
The simplified form of the complex rational expression is \( \frac{x}{4(x - 4)} - \frac{1}{x - 4} \)
1Step 1: Rewrite the Expression
Rewrite the complex rational expression as a division problem. Hence, the expression becomes \( \frac{x}{4} - 1 ÷ x - 4 \).
2Step 2: Multiply By the Reciprocal
To simplify this expression, find the reciprocal of the denominator and multiply the expression in the numerator by the reciprocal. The reciprocal of \( x - 4 \) is \( \frac{1}{x - 4} \), resulting to \( \left(\frac{x}{4} - 1\right) * \frac{1}{x - 4} \)
3Step 3: Simplify the Expression
Distribute \( \frac{1}{x - 4} \) to \( \frac{x}{4} \) and -1, leading to \( \frac{x}{4(x - 4)} - \frac{1}{x - 4} \).