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Chapter 7: Problem 55

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x}{x+1}$$

Short Answer

Expert verified
The rational expression \(\frac{x}{x+1}\) cannot be simplified further.

Step by step solution

01

Analysis

First, observe the given rational expression \(\frac{x}{x+1}\). We know that a rational expression can be simplified if there are common factors in the numerator and the denominator.
02

Identifying Common Factors

In this rational expression, the numerator is \(x\) and the denominator is \(x+1\). There are no common factors in the numerator and the denominator, other than 1.
03

Conclusion

Since there are no common factors in the numerator and the denominator of the given fraction, other than 1, the rational expression \(\frac{x}{x+1}\) cannot be simplified further.

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Most popular questions from this chapter

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{(y-3)(y+2)}{(y+1)(y-4)}-\frac{(y+2)(y+3)}{(y+1)(4-y)}-\frac{(y+5)(y-1)}{(y+1)(4-y)}$$

If the ratio of the corresponding sides of two similar triangles is 1 to 1 ( \(\frac{1}{1}\) ), what must be true about the triangles?

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

add or subtract as indicated. Simplify the result, if possible. $$\begin{aligned} &\frac{x^{2}+9 x}{4 x^{2}-11 x-3}+\frac{3 x-5 x^{2}}{4 x^{2}-11 x-3}\\\ &x^{2}-4 x-4 x-4 \end{aligned}$$

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{10}{x-2}-\frac{6}{2-x}$$
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