Problem 61
Question
Simplify each complex rational expression. $$\frac{1+\frac{1}{x}}{3-\frac{1}{x}}$$
Step-by-Step Solution
Verified Answer
The simplified form of the complex rational expression is \( \frac{x+1}{3x-1} \)
1Step 1: Distribute the Common Denominator to Every Term
Multiply the entire expression by \(x\) to clear the fractions in the numerator and the denominator. This results in:\[\frac{x(1+\frac{1}{x})}{x(3-\frac{1}{x})} = \frac{x+1}{3x-1}\]
2Step 2: Simplification
The expression simplified in step one does not simplify any further. The answer is \( \frac{x+1}{3x-1} \)
Other exercises in this chapter
Problem 61
Evaluate each expression or indicate that the root is not a real number. $$\sqrt[4]{(-3)^{4}}$$
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Perform the indicated operations Indicate the degree of the resulting polynomial. $$ \left(4 x^{2} y+8 x y+11\right)+\left(-2 x^{2} y+5 x y+2\right) $$
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Simplify each exponential expression in Exercises 23–64. $$\left(\frac{-15 a^{4} b^{2}}{5 a^{10} b^{-3}}\right)^{3}$$
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Factor using the formula for the sum or difference of tho cubes. $$ 27 x^{3}-1 $$
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