Problem 76 - College Algebra

Question

Perform the indicated operations. Simplify the result, if possible. $$\left(4-\frac{3}{x+2}\right)\left(1+\frac{5}{x-1}\right)$$

Step-by-Step Solution

Answer

The simplified result is \(4+ \frac{5x - 23}{(x+2)(x-1)}\).

Step 1: Multiplication of Expressions

To multiply the expressions, apply the distributive property which entails multiplying each term in the first bracket by each term in the second bracket. You will get: \(4 + \frac{20}{x-1} - \frac{3}{x+2} - \frac{15}{(x+2)(x-1)}. \)

Step 2: Simplification

To simplify, find a common denominator to combine the fraction terms. The common denominator here would be \((x+2)(x-1)\). Rewrite each fraction term with this common denominator. The expression will be: \(4+ \frac{20(x+2)}{(x+2)(x-1)} - \frac{3(x-1)}{(x+2)(x-1)} - \frac{15}{(x+2)(x-1)}\). Combine the terms with common denominators, and simplify the result by factoring and cancelling common terms.