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Q:
Simplify the following expressions completely:
\( \frac{1-\frac{1}{x+1}}{1+\frac{1}{x^{2}-1}} \)
Q:
Rationalize the Denominator:
\( \frac{2+\sqrt{3}}{7+\sqrt{3}} \)
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Q:
Solve by completing the square. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.
\[ r^{2}-5 r=1 \]
Q:
11. จงหาเซตคำตอบของอสมการต่อไปนี
\[ 11.1 x^{2}-5 x+6<0 \]
\( 11.2 x^{2}+2 x-15 \geq 0 \)
Q:
Solve. First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by completing the square. (Enter your answers as a comma-separated list.)
\[ x^{2}-x-1=0 \]
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Q:
4.Сократите дробь:1) \( \left.\frac{5-\sqrt{5}}{10-5 \sqrt{2}} ; 2\right) \frac{9 a-b^{2}}{9 a-6 b \sqrt{a}+b^{2}} \)
3) \( \frac{m-6}{\sqrt{m}-\sqrt{6}} \)
Q:
Perform the following operation and express in simplest form.
\[ \frac{x-1}{x^{2}+5 x-6} \div \frac{7 x-56}{x^{2}-2 x-48} \]
Q:
\( \sqrt {x}+\sqrt {x+7}+2\sqrt {x^{2}+7x}<35-2x \)
Q:
\( 2 b . \log _{\mathrm{a}} \mathrm{b} \times \log _{\mathrm{b}} \mathrm{c}= \) ?
Q:
Solve by completing the square. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
\[ z^{2}=9 z+1 \]
\( z=\square \)
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