\(C=\dfrac{\dfrac{1}{2}-cos2a}{\dfrac{\sqrt{3}}{2}+sin2a}=\dfrac{cos\dfrac{\pi}{3}-cos2a}{sin\dfrac{\pi}{3}+sin2a}=\dfrac{-2sin\left(a+\dfrac{\pi}{6}\right)sin\left(\dfrac{\pi}{6}-a\right)}{2sin\left(a+\dfrac{\pi}{6}\right)cos\left(\dfrac{\pi}{6}-a\right)}=-tan\left(\dfrac{\pi}{6}-a\right)=tan\left(a-\dfrac{\pi}{6}\right)\)

d: \(\left(x-2\right)\left(x^2+2x+4\right)\left(x+2\right)\left(x^2-2x+4\right)\)

\(=\left(x^3-8\right)\left(x^3+8\right)\)

\(=x^6-64\)

#)Giải :

\(A=\frac{3^{10}.11+3^{10}.5}{3^9.2^4}=\frac{3^{10}\left(11+5\right)}{3^9.2^4}=\frac{3^{10}.2^4}{3^9.2^3}=3\)

\(A=\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)

\(A=\frac{3^{10}\left(11+5\right)}{3^9.2^4}\)

\(A=\frac{3^{10}.16}{3^9.2^4}\)

\(A=\frac{3^{10}.2^4}{3^9.2^4}\)

\(A=3\)

c: \(\left(2x+3\right)^2+\left(2x-3\right)^2-\left(2x+3\right)\left(2x-3\right)\)

\(=4x^2+12x+9+4x^2-12x+9-\left(4x^2-9\right)\)

\(=8x^2+18-4x^2+9=4x^2+27\)

d: \(\left(x-1\right)\cdot\left(x^2+x+1\right)-\left(2x+3\right)\left(4x^2-6x+9\right)\)

\(=\left(x-1\right)\left(x^2+x\cdot1+1^2\right)-\left(2x+3\right)\left[\left(2x\right)^2-2x\cdot3+3^2\right]\)

\(=x^3-1-8x^3-27=-7x^3-28\)

e: \(\left(x+1\right)^3-\left(x-1\right)^3-6x^2\)

\(=x^3+3x^2+3x+1-6x^2-\left(x^3-3x^2+3x-1\right)\)

\(=x^3-3x^2+3x+1-x^3+3x^2-3x+1\)

=2

Sửa: \(C=\left(\dfrac{\sqrt{x}+1}{x-4}-\dfrac{\sqrt{x}-1}{x+4\sqrt{x}+4}\right)\cdot\dfrac{x\sqrt{x}+2x-4\sqrt{x}-8}{\sqrt{x}}\)

\(C=\dfrac{\sqrt{x}+3\sqrt{x}+2-x+3\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)^2}\cdot\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)^2}{\sqrt{x}}\\ C=\dfrac{6\sqrt{x}}{\sqrt{x}}=6\)

\(\dfrac{25}{30}=\dfrac{5}{7};\dfrac{9}{15}=\dfrac{3}{5};\dfrac{6}{10}=\dfrac{3}{5};\dfrac{10}{12}=\dfrac{5}{6}\)

tự xem cái nào giống

a) \(\dfrac{3}{5};\dfrac{5}{6}\) : phân số tối giản
\(\dfrac{25}{30}=\dfrac{25:5}{30:5}=\dfrac{5}{6}\)
\(\dfrac{9}{15}=\dfrac{9:3}{15:3}=\dfrac{3}{5}\)
\(\dfrac{10}{12}=\dfrac{10:2}{12:2}=\dfrac{5}{6}\)
\(\dfrac{6}{10}=\dfrac{6:2}{10:2}=\dfrac{3}{5}\)
b) \(\dfrac{3}{5}=\dfrac{9}{15}=\dfrac{6}{10}\) ; \(\dfrac{5}{6}=\dfrac{25}{30}=\dfrac{10}{12}\)

b: \(\Leftrightarrow n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{0;-2;1;-3;3;-5\right\}\)

c: \(\Leftrightarrow n+2\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{-1;-3;3;-7\right\}\)

d: \(\Leftrightarrow n+2\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{-1;-3;0;-4;2;-6\right\}\)

a: \(\Leftrightarrow n-1\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{2;0;6;-4\right\}\)

21/15=21:3/15:3=7/5

11/121=11:11/121:11=1/11

27/72=27:9/72:9=3/8

\(\dfrac{21}{15}=\dfrac{7}{5};\dfrac{11}{121}=\dfrac{1}{11};\dfrac{27}{72}=\dfrac{3}{8}\)

\(\dfrac{21}{15}=\dfrac{21:3}{15:3}=\dfrac{7}{5}\)

\(\dfrac{11}{121}=\dfrac{11:11}{121:11}=\dfrac{1}{11}\)

\(\dfrac{27}{72}=\dfrac{27:9}{72:9}=\dfrac{3}{8}\)

\(A=\frac{132639}{173451}\)

\(A=\frac{132639:10203}{173451:10203}\)

\(A=\frac{13}{17}\)

\(B=\frac{16515}{20919}\)

\(B=\frac{16515:1101}{20919:1101}\)

\(B=\frac{15}{19}\)