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Chapter 7: Problem 35

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{2 y-10}{3 y-15}$$

Short Answer

Expert verified
The simplified form of the rational expression \(\frac{2y - 10}{3y - 15}\) is \(\frac{2}{3}\).

Step by step solution

01

Identify Common Factors in Numerator and Denominator

Examine both the numerator which is '2y - 10' and the denominator '3y - 15' for common factors. It's clear that both terms in the numerator can be divided by '2', and both terms in the denominator can be divided by '3'.
02

Factor Out Common Factors

Factor out the common factors identified in Step 1 from the numerator and the denominator. Therefore, the expression is rewritten like this: \(\frac{2(y - 5)}{3(y - 5)}\).
03

Cancel Common Factor from Numerator and Denominator

In this step, cancel out the common term '(y - 5)' from both the numerator and the denominator. This is in accordance with the simplification rule that a term in the numerator and the same term in the denominator cancels each other out to become 1.
04

Write the Simplified Rational Expression

After simplifying, the rational number becomes \(\frac{2}{3}\). This is the most simplified form.

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Most popular questions from this chapter

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3}{x-2}+\frac{4}{x+3}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6}{x-5}+\frac{2}{5-x}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{4}{x}+\frac{3}{x-5}$$

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. $$\frac{3 x+6}{2}-\frac{x}{2}=x+3$$

perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{2}+\frac{2}{3}$$
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