Question

Scrieţi sub formă de raport algebric ireductibil:
3a+2  :   4+6a
-------     -------
 a-√3     5a²-15
Ajutaţi-mă vă rog mult.La nivel de cl.7

Answer 1

4+6a = 2(2+3a) = 2(3a+2)

5a² - 15 = 5(a²-3) = 5[a² - (√3)²] = 5(a-√3)(a+√3)

[tex]\it \dfrac{3a+2}{a-\sqrt3} :\dfrac{4+6a}{5a^2-15} = \dfrac{3a+2}{a-\sqrt3} \cdot\dfrac{5a^2-15}{4+6a} = \\\;\\ \\\;\\ \dfrac{3a+2}{a-\sqrt3} \cdot\dfrac{5(a-\sqrt3)(a+\sqrt3)}{2(3a+2)} = \dfrac{5(a+\sqrt3)}{2} [/tex]