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Chapter 7: Problem 61

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

Short Answer

Expert verified
The simplified rational expression is -1.

Step by step solution

01

Observe and Re-write

First, observe the expression \(\frac{2x-3}{3-2x}\). It is noticed that if you factor out -1 from the denominator we see that the two expressions are negatives of each other. Thus, rewrite the expression as \(\frac{2x-3}{-(2x-3)}\).
02

Cancel Common Terms

In this step, cancel the common terms in the numerator and the denominator. Since both the numerator and the denominator are the same, except for the negative sign, the entire expression reduces to -1.

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Most popular questions from this chapter

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve \(\frac{x}{9}=\frac{4}{6}\) by using the cross-products principle or by multiplying both sides by \(18,\) the least common denominator.

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. $$\frac{x^{2}-13}{x+4}-\frac{3}{x+4}=x+4, x \neq-4$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-2}{x^{2}-25}-\frac{x-2}{25-x^{2}}$$

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

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