Calcul algébrique : Test de niveau 2

Calculez \(\dfrac{3x+3y}{x^2-y^2}+\dfrac{7x-7y}{x^2-2xy+y^2}\).

Calculez \(\left(\dfrac{4}{-15}-\dfrac{7}{-18}\right)-\left(\dfrac{1}{15}-\dfrac{1}{9}\right)\).

Calculez \(\dfrac{3}{4}-\left(\dfrac{1}{4}-\left(\dfrac{2}{3}-\dfrac{3}{4}\right)\right)\)

Calculez \(\left(\dfrac{1}{x}+\dfrac{1}{y}\right)/\left(\dfrac{1}{x^2}-\dfrac{1}{y^2}\right)\).

Si \(a=0,2\), \(b=-0,1\) et  \(c=-0,5\), calculez \((\frac{a}{b}+\frac{b}{c})\cdot \frac{c}{a}\).

Calculez \(\dfrac{a-b}{b}-\dfrac{a+b}{2b}-1\).

Si \(a=0,2\), \(b=-0,1\) et  \(c=-0,5\), calculez \((\frac{a+c}{b})/(\frac{a}{b}+c)\).

Simplifiez l'expression \(\left( \dfrac{a^2b^3c^{-2}}{a^3b^2c}\right) ^{-1}\).

Simplifiez l'expression \(\sqrt[4]{a^4+a^4b}\).

Calculez \(\sqrt[8]{a^6}\sqrt[12]{a^5}\sqrt[6]{a}\).