\(y=\dfrac{sinx-cosx}{sinx+cosx}\Rightarrow y'=\dfrac{\left(sinx-cosx\right)'.\left(sinx+cosx\right)-\left(sinx+cosx\right)'.\left(sinx-cosx\right)}{\left(sinx+cosx\right)^2}\)

Dễ thấy : \(\left(sinx-cosx\right)'=cosx+sinx\)

\(\left(sinx+cosx\right)'=cosx-sinx\)

Suy ra : \(y'=\dfrac{\left(sinx+cosx\right)^2+\left(sinx-cosx\right)^2}{\left(sinx+cosx\right)^2}=\dfrac{2}{\left(sinx+cosx\right)^2}\)

\(\dfrac{3}{4}.\dfrac{10}{9}-\dfrac{5}{11}=\dfrac{5}{6}-\dfrac{5}{11}=\dfrac{25}{66}\)

\(3-4x-x^2=7-\left(x^2+4x+4\right)=7-\left(x+2\right)^2\le7\forall x\)

" = " \(\Leftrightarrow x+2=0\Leftrightarrow x=-2\)

Vậy ... 

Dễ thấy : \(x^2+4x+10=\left(x+2\right)^2+6\ge6\forall x\)

\(\Rightarrow\dfrac{3}{x^2+4x+10}\le\dfrac{3}{6}=\dfrac{1}{2}\) 

" = " \(\Leftrightarrow x+2=0\Leftrightarrow x=-2\)

Vậy ... 

\(\dfrac{3}{7}-\dfrac{2}{9}+\dfrac{1}{2}=\dfrac{54}{126}-\dfrac{28}{126}+\dfrac{63}{126}=\dfrac{89}{126}\)

\(a.\dfrac{5}{6}.\dfrac{3}{10}=\dfrac{5.3}{3.2.5.2}=\dfrac{1}{4}\)

b  \(8.\dfrac{7}{24}=8.\dfrac{7}{8.3}=\dfrac{7}{3}\) 

c. \(\dfrac{3}{7}:\dfrac{6}{35}=\dfrac{3}{7}.\dfrac{35}{6}=\dfrac{3}{7}.\dfrac{5.7}{3.2}=\dfrac{5}{2}\)

d. \(\dfrac{8}{9}:4=\dfrac{8}{9}.\dfrac{1}{4}=\dfrac{2}{9}\)

\(Tử=8.75.3+6.25.4-240=24\left(75+25\right)-240=24.100-240=24.90\)

Mẫu = \(15.2.6+18.16.5=18.10+18.80=18.90\)

Tử / Mẫu = \(\dfrac{24}{18}=\dfrac{4}{3}\)

Đẹp 

giỏi quá pro vip

= 19