Problem 79 - College Algebra Essentials

Question

Perform the indicated operations. Simplify the result, if possible. $$\left(\frac{1}{a^{3}-b^{3}} \cdot \frac{a c+a d-b c-b d}{1}\right)-\frac{c-d}{a^{2}+a b+b^{2}}$$

Step-by-Step Solution

Answer

The simplified expression is \[\frac{a c+a d-b c-b d}{a^3-b^3} - \frac{c-d}{a^2+a b+b^2}\].

Step 1: Simplify First Fraction

We start by simplifying the first fraction. This involves dividing \((a c+a d-b c-b d)\) by 1. This just gives us \((a c+a d-b c-b d)\). So, the first fraction simplifies to \(\frac{a c+a d-b c-b d}{a^3-b^3}\).

Step 2: Simplify Second Fraction

The second fraction is already in simplest form, so we can move to the next step.

Step 3: Perform Subtraction

Now we just subtract our second fraction from the first. This gives us our final answer: \[\frac{a c+a d-b c-b d}{a^3-b^3} - \frac{c-d}{a^2+a b+b^2}\]