Problem 60 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The simplified form of the given complex rational expression is \(\frac{1}{4}\).

Step 1: Distribute the Denominator

Multiply both the numerator and the denominator of the complex fraction by the denominator of the simple fraction in the numerator. In this case, multiply by \(4\):\[(4)\left(\frac{x}{4}-1\right)\div (4)\left(x-4\right)\]

Step 2: Simplify

Simplify by cancelling the 4 in the numerator and multiplying the denominator by \(4\). This results in:\[ \left(x-4\right) \div \left(4x-16\right)\]

Step 3: Factor the Terms

Factor out the greatest common factor from the denominator, which in this case is \(4\):\[(x-4) \div 4\left(x-4\right)\]

Step 4: Cancel Out Common Terms

Finally, we can cancel out the \(x-4\) term in the numerator and the denominator of our complex fraction. This gives us:\[\frac{1}{4} \]