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Chapter 0: Problem 62

Simplify each complex rational expression. $$\frac{8+\frac{1}{x}}{4-\frac{1}{x}}$$

Short Answer

Expert verified
The simplified form of the given complex rational expression is \(\frac{8x+1}{4x-1}\)

Step by step solution

01

Determine LCD and rewrite the expression

The least common denominator (LCD) in the equation is \(x\). Rewrite the expression to achieve a simplified denominator on both fractions by multiplying each part of the expression by the LCD. This gives: \(x * \frac{8+\frac{1}{x}}{4-\frac{1}{x}} = \frac{8x+1}{4x-1}\)
02

Simplify the result

The fraction generated from Step 1 doesn鈥檛 simplify any further. So the final answer will be \(\frac{8x+1}{4x-1}\).

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Most popular questions from this chapter

$$\text { Factor completely.}$$ $$10 x^{2}(x+1)-7 x(x+1)-6(x+1)$$

$$\text { factor completely.}$$ $$x^{4}-y^{4}-2 x^{3} y+2 x y^{3}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I factored \(4 x^{2}-100\) completely and obtained \((2 x+10)(2 x-10)\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$8^{-\frac{1}{3}}=-2$$

$$\text { Factor completely.}$$ $$(x+y)^{4}-100(x+y)^{2}$$
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