Problem 68 - Introductory Algebra for College Students

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{9-15 x}{5 x^{2}-3 x}$$

Step-by-Step Solution

Answer

The final simplified form of the expression is \(3/x\)

Step 1: Factorize the numerator

The numerator \(9-15x\) can be factorized if we take out the common factor -3, thus it becomes -3(3-5x).

Step 2: Factorize the denominator

In the denominator \(5x^{2}-3x\), the common factor x can be factored out, which results in x(5x-3).

Step 3: Simplify the rational expression

Now let's simplify the rational expression \(-3(3-5x) / x(5x-3)\) by reducing same terms from numerator and denominator. This gives \(-3(-1) / x(-1)\)

Step 4: Final Simplification

Simplifying we get: \(3/x\) which is the final simplified form of the given expression.