Problem 66 - Introductory Algebra for College Students

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{9 x-15}{5-3 x}$$

Step-by-Step Solution

Answer

The simplified form of the rational expression \(\frac{9x - 15}{5 - 3x}\) is \(-3\).

Step 1: Factorizing Numerator and Denominator

The first step is to factorise the numerator and denominator separately. From the numerator \(9x - 15\), taking 3 as common yields \(3(3x - 5)\). In the denominator, \(5 - 3x\) can be rewritten as \(-1*(3x - 5)\) by taking -1 common.

Step 2: Canceling Common Factors

The rational expression after factorization becomes \(\frac{3(3x - 5)}{-1*(3x - 5)}\). Now both the numerator and the denominator have a common term \((3x - 5)\), which can be cancelled from the top and bottom.

Step 3: Final Result

After cancelling the common terms, the simplified expression becomes \(-3\). This is the simplest form of the original expression.