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Chapter 7: Problem 45
Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{2 x+3}{2 x+5}$$
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add or subtract as indicated. Simplify the result, if possible. $$\begin{aligned} &\frac{x^{2}+9 x}{4 x^{2}-11 x-3}+\frac{3 x-5 x^{2}}{4 x^{2}-11 x-3}\\\ &x^{2}-4 x-4 x-4 \end{aligned}$$
The temperature, in degrees Fahrenheit, of a dessert placed in a freezer for \(t\) hours is modeled by $$ \frac{t+30}{t^{2}+4 t+1}-\frac{t-50}{t^{2}+4 t+1} $$ a. Express the temperature as a single rational expression. b. Use your rational expression from part (a) to find the temperature of the dessert, to the nearest hundredth of a degree, after 1 hour and after 2 hours.
denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{y-3}{y^{2}-25}+\frac{y-3}{25-y^{2}}$$
use the GRAPH or TABLE feature of a graphing utility to determine if the subtraction has been performed correctly. If the answer is wrong, correct it and then verify your correction using the graphing utility. $$\frac{3 x+6}{2}-\frac{x}{2}=x+3$$
denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{6 x+5}{x-2}+\frac{4 x}{2-x}$$
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