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Chapter 0: Problem 73
Contain fractional expressions that occur frequently in calculus. Simplify each expression. $$\frac{\sqrt{x}-\frac{1}{3 \sqrt{x}}}{\sqrt{x}}$$
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Perform the indicated operations. $$\frac{1}{x^{n}-1}-\frac{1}{x^{n}+1}-\frac{1}{x^{2 n}-1}$$
In solving \(\sqrt{2 x-1}+2=x,\) why is it a good idea to isolate the radical term? What if we don't do this and simply square each side? Describe what happens.
Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A company manufactures and sells personalized stationery. The weekly fixed cost is \(\$ 3000\) and it costs \(\$ 3,00\) to produce cach package of stationery. The selling price is \(\$ 5.50\) per package. How many packages of stationery must be produced and sold each week for the company to generate a profit?
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I evaluated \(\frac{3 x-3}{4 x(x-1)}\) for \(x=1\) and obtained 0.
Explain how to add rational expressions having no common factors in their denominators. Use \(\frac{3}{x+5}+\frac{7}{x+2}\) in your explanation.
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