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Chapter 7: Problem 30

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{-21}{7 x-14}$$

Short Answer

Expert verified
The simplified form of the rational expression \(\frac{-21}{7x - 14}\) is \(\frac{-3}{x - 2}\).

Step by step solution

01

Factorize the numerator and denominator

The expression can be rewritten as \(\frac{-3 \times 7}{7 \times (x - 2)}\). The factorization will assist with the identification of common factors.
02

Cancel out common factors from the numerator and denominator

As we can notice, 7 is a common factor in the numerator and denominator. So, we eliminate it, which leaves us with \(\frac{-3}{x -2}\).
03

Spot if any more simplification is possible

We verify if there are any more common factors or similar terms to simplify further. As there are no more common factors, this expression is simplified to the fullest.

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Most popular questions from this chapter

Subtract: \(\frac{13}{15}-\frac{8}{45}\) (Section 1.2, Example 9)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x^{2}-2}{x^{2}+6 x-7}+\frac{19-4 x}{7-6 x-x^{2}}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x}{x+6}-1$$

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

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