2) Calculer puis écrire sans radical au dénominateur les expressions suivantes : \( C=\frac{\sqrt{3}}{\sqrt{3}+1}-\frac{\sqrt{3}-1}{\sqrt{3}+2}- \) et \( D=\left(\sqrt{5}+\frac{1}{\sqrt{5}}\right)^{2} \) 3) Soient \( x, y \) et \( z \) trois nombres réels strictement positifs. a) Montre que si \( x y+y z+x z=0 \) alors \( \frac{y+z}{x}+\frac{x+z}{y}+\frac{x+y}{z}=-3 \). b) Montrer que si \( x<y \) alors \( \sqrt{x+y+2 \sqrt{x y}}+\sqrt{x+y-2 \sqrt{x y}}=2 \sqrt{y} \) c) Montrer que si \( x \geq 2 \) alors \( (\sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}})^{2}=4(x-1) \)

83 Olivia drove 170 miles each way (there and back) to visit her cousin. On the trip, Olivia drove an extra 20 miles to see the Grand Canyon. She also drove an extra 45 miles to see Lake Powell. Write one or more equations you could use to represent the total number of miles Olivia drove on her trip. Show your work.

4. \( \frac{(4 n)!+(4 n+1)!}{(4 n+1)!-(4 n)!} \) ifadesinin eşiti aşağıdakilerden han- gisidir? \( \begin{array}{ll}\text { A) } \frac{2 n+1}{2} & \text { B) } \frac{2 n+1}{n} \\ \text { C) } \frac{2 n+1}{2 n} & \text { D) } \frac{2 n}{2 n+1}\end{array} \)

A straight highway connects Town A and Town B, a distance of 45 kilometres, Andy started biking along the highway from Town A to Town B at 8:00 AM at a constant speed of 3 kilometres per hour. Ben started biking on a parallel highway from Town B to Town A at 9:00 AM at a constant speed of 4 kilometres per hour. How many kilometres had Ben biked when they met along the way?

\[ \frac{(2 n-3)!\cdot(3 n-3)!}{(2 n-1)!\cdot(3 n-4)!}=\frac{1}{14} \] olduğuna göre, \( n \) kaçtır?

Reducir los siguientes polinomios \[ \frac{2}{3} a+\frac{4}{3} a+\frac{5}{4} a+\frac{2}{3} b+\frac{5}{2} b \]