Problem 43 - Introductory Algebra for College Students

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{2 y^{2}-7 y+3}{2 y^{2}-5 y+2}$$

Step-by-Step Solution

Answer

The simplified form of the given rational expression is \(\frac{y - 3}{y - 2}\).

Step 1: Factorization of the Numerator

Factorize the numerator \(2y^2 - 7y + 3\). In this case, it can be written as \((2y - 1)(y - 3)\).

Step 2: Factorization of the Denominator

Factorize the denominator \(2y^2 - 5y + 2\). It can be written as \((2y - 1)(y - 2)\).

Step 3: Simplification of the Rational Expression

After factorization, the given expression becomes \(\frac{(2y - 1)(y - 3)}{(2y - 1)(y - 2)}\). The term \((2y - 1)\) appears in both the numerator and the denominator, so they can be cancelled out to simplify the expression, resulting in \(\frac{y - 3}{y - 2}\).