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Magazine Problem 25
Find all complex solutions for each equation by hand. $$\frac{1}{x+2}+\frac{3}{x+7}=\frac{5}{x^{2}+9 x+14}$$
Problem 25
Use positive rational exponents to rewrite each expression. Assume variables represent positive numbers. $$(\sqrt[4]{y})^{-3}$$
Problem 26
Explain how the graph of \(f\) can be obtained from the graph of \(y=\frac{1}{x}\) or \(y=\frac{1}{x^{2}} .\) Draw a sketch of the graph of \(f\) by hand. Then generate an accurate depiction of the graph with a graphing calculator. Finally, give the domain and range. $$f(x)=\frac{1}{x^{2}}+3$$
Problem 26
Write a formula for a rational function with vertical asymptote \(x=1\) and oblique asymptote \(y=x+2\)
Problem 26
Use positive rational exponents to rewrite each expression. Assume variables represent positive numbers. $$(\sqrt[3]{y^{2}})^{-5}$$
Problem 26
Find all complex solutions for each equation by hand. $$\frac{1}{x+3}+\frac{4}{x+5}=\frac{2}{x^{2}+8 x+15}$$
Problem 26
Solve each equation by hand. Do not use a calculator. $$2 x^{-2}-x^{-1}=3$$
Problem 27
Explain how the graph of \(f\) can be obtained from the graph of \(y=\frac{1}{x}\) or \(y=\frac{1}{x^{2}} .\) Draw a sketch of the graph of \(f\) by hand. Then generate an accurate depiction of the graph with a graphing calculator. Finally, give the domain and range. $$f(x)=-\frac{2}{x^{2}}$$
Problem 27
Use positive rational exponents to rewrite each expression. Assume variables represent positive numbers. $$\sqrt{x} \cdot \sqrt[3]{x}$$
Problem 27
Find all complex solutions for each equation by hand. $$\frac{x}{x-3}+\frac{4}{x+3}=\frac{18}{x^{2}-9}$$
