Question

Determinați x∈R pentru care $\frac{x-2}{2x+3}$+$\frac{x+2}{2x-3}$=4

Answer 1

avem [(2x-3)(x-2)+(x+2)(2x+3)]/(4x²-9)=4
2x²-4x-3x+6+2x²+3x+4x+6=4(4x²-9)
4x²+12=16x²-36
4x²-16x²=-36-12
-12x²=-48      inmultim -1
12x²=48
x²=48/12
x1=√4=2
x2=-√4=-2
S={-2,2}