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Chapter 7: Problem 43

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

Short Answer

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

Step by step solution

01

Factorization of the Numerator

Factorize the numerator \(2y^2 - 7y + 3\). In this case, it can be written as \((2y - 1)(y - 3)\).
02

Factorization of the Denominator

Factorize the denominator \(2y^2 - 5y + 2\). It can be written as \((2y - 1)(y - 2)\).
03

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 \(\frac{y - 3}{y - 2}\).

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Most popular questions from this chapter

use the GRAPH or TABLE feature of a graphing utility to determine if the subtraction has been performed correctly. If the answer is wrong, correct it and then verify your correction using the graphing utility. $$\frac{x^{2}+4 x+3}{x+2}-\frac{5 x+9}{x+2}=x-2, x \neq-2$$

What is the relationship among time traveled, distance traveled, and rate of travel?

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{y-7}{y^{2}-16}+\frac{7-y}{16-y^{2}}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{2}{x-1}+\frac{3}{x+2}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{7}{x}+4$$
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