Câu 2.Cho tanalpha =3 Tính giá trị của biểu thức P=(2sinalpha +3cosalpha )/(sinalpha +cosalpha ) A. 2. B. (9)/(4) (Are) C. (5)/(2) D . 2024.

Given that $\tan \alpha = 3$, we have $\frac{\sin \alpha}{\cos \alpha} = 3$, which means $\sin \alpha = 3 \cos \alpha$.<br /><br />Now let's substitute this into the expression for P:<br />$$P = \frac{2\sin \alpha + 3\cos \alpha}{\sin \alpha + \cos \alpha} = \frac{2(3\cos \alpha) + 3\cos \alpha}{3\cos \alpha + \cos \alpha} = \frac{6\cos \alpha + 3\cos \alpha}{4\cos \alpha} = \frac{9\cos \alpha}{4\cos \alpha}$$<br /><br />Assuming $\cos \alpha \neq 0$, we can cancel $\cos \alpha$ from the numerator and denominator:<br />$$P = \frac{9}{4}$$<br /><br />Therefore, the value of the expression P is $\frac{9}{4}$.<br /><br />Final Answer: The final answer is $\boxed{B}$