Chapter 11: Problem 1
Write the extremes and the means of the proportion \(\frac{3}{4}=\frac{9}{12}\).
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Simplify the expression. (Review \(8.3 \text { for } 11.7)\) $$\frac{5}{10 x}$$
Completely factor the expression. $$3 x^{3}+21 x^{2}+30 x$$
Simplify the expression. $$\frac{2 x}{x-1}-\frac{7 x}{x+4}$$
When you add rational expressions, you may need to factor a trinomial to find the LCD. Study the sample below. Then simplify the expressions in Exercises 46–49. $$\text { Sample: } \frac{2 x}{x^{2}-1}+\frac{3}{x^{2}+x-2}=\frac{2 x}{(x+1)(x-1)}+\frac{3}{(x-1)(x+2)}$$ The LCD is \((x+1)(x-1)(x+2)\) Note: If you just used \(\left(x^{2}-1\right)\left(x^{2}+x-2\right)\) as the common denominator, the factor \((x-1)\) would be included twice. $$\frac{7 x+2}{16-x^{2}}+\frac{7}{x-4}$$
Simplify the radical expression. $$\sqrt{\frac{11}{9}}$$
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