Question

Rezolvati in R ecuatia $\frac{x-7}{3x+1} = \frac{x}{x-3}$

Answer 1

Punem conditiile ca : 
3x+1 ≠ 0 ⇒ 3x ≠ -1 ⇒ x ≠ $\frac{-1}{3}$
x- 3 ≠ 0 ⇒ x ≠ - 3
Apoi rezolvam :
Facem produsele pe diagonala : (x-7)(x-3)=x(3x+1)
Facem inmultirile : x² - 3x - 7x + 21 = 3x² + x
Trecem toti termenii intr-o parte : 2x² +11x - 21 = 0
Facem delta : 121 + 168 = 289 si √Δ= 17.
x1 = $\frac{-11+17}{4}$ = $\frac{3}{2}$
x2 = $\frac{-11-17}{4}$ = $\frac{-28}{4}$ = -7