P= [tex]\left ( \frac{a^{\frac{1}{2}}+2}{a+2a^{\frac{1}{2}}+1} -\frac{a^{\frac{1}{2}}-2}{a-1}\right ) \ast \frac{\left ( a^{\frac{1}{2}}+1 \right )}{a^{\frac{1}{2}}} , \left ( a>0 ,a\neq \pm1 \right )[/tex]
Đặt [tex]a^{\frac{1}{2}}=t\Rightarrow \sqrt{a}=t\Rightarrow a=t^{2}[/tex] (Do a>0 nên [tex]a^{\frac{1}{2}}=\sqrt{a}[/tex])
Sau khi đặt ta có phương trình:
[tex]\left ( \frac{t+2}{t^{2}+2t+1}-\frac{t-2}{t^{2}-1} \right )*\frac{t+1}{t}[/tex]
[tex]=\left ( \frac{t+2}{\left ( t+1 \right )^{2}}-\frac{t-2}{\left ( t-1 \right )*\left ( t+1 \right )} \right )*\frac{t+1}{t}[/tex]
[tex]=\left ( \frac{\left ( t+2 \right )*\left ( t-1 \right )-\left ( t-2 \right )*\left ( t+1 \right )}{\left ( t+1 \right )^{2}*\left ( t-1 \right )} \right )*\frac{t+1}{t}[/tex]
[tex]=\frac{t^{2}+t-2-t^{2}+t+2}{\left ( t+1 \right )^{2}*\left ( t-1 \right )}*\frac{t+1}{t}[/tex]
[tex]=\frac{2t}{\left ( t+1 \right )^{2}*\left ( t-1 \right )}*\frac{t+1}{t}[/tex]
[tex]=\frac{2}{\left ( t+1 \right )*\left ( t-1 \right )}=\frac{2}{t^{2}-1}[/tex] (mà [tex]a=t^{2}[/tex] do ta đặt)
[tex]=\frac{2}{a-1}[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
