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![[tex]\underbrace{\frac{t^2}{t^2-1}}_{A}=\underbrace{-\frac{1}{2(t+1)}+\frac{1}{2(t-1)}+1}_{B}[/tex]](images/latex/8c8e1a812fa99997a86a4d76a65dbea5adf3d260_0.png "[tex]\underbrace{\frac{t^2}{t^2-1}}_{A}=\underbrace{-\frac{1}{2(t+1)}+\frac{1}{2(t-1)}+1}_{B}[/tex]")
![[tex]\frac{{ - 1}}{{2(t + 1)}} + \frac{1}{{2(t - 1)}} + 1[/tex]](images/latex/bf5fe59fe7f0063451c317c8e1677db1ff54357e_0.png "[tex]\frac{{ - 1}}{{2(t + 1)}} + \frac{1}{{2(t - 1)}} + 1[/tex]")
![[tex]\frac{{\frac{{ - 1}}{2}}}{{(t + 1)}}.\frac{{(t - 1)}}{{(t - 1)}} + \frac{{\frac{1}{2}}}{{2(t - 1)}}.\frac{{(t + 1)}}{{(t + 1)}} + 1[/tex]](images/latex/dd8d55853ab820cbc3e62a9f8d564f197bb72afb_0.png "[tex]\frac{{\frac{{ - 1}}{2}}}{{(t + 1)}}.\frac{{(t - 1)}}{{(t - 1)}} + \frac{{\frac{1}{2}}}{{2(t - 1)}}.\frac{{(t + 1)}}{{(t + 1)}} + 1[/tex]")
![[tex]\frac{{ - \frac{1}{2}t + \frac{1}{2}}}{{t^2 - 1}} + \frac{{\frac{1}{2}t + \frac{1}{2}}}{{t^2 - 1}} + \frac{{t^2 - 1}}{{t^2 - 1}}[/tex]](images/latex/cd3f19dc177e14de004b7d720f67af1defa8619e_0.png "[tex]\frac{{ - \frac{1}{2}t + \frac{1}{2}}}{{t^2 - 1}} + \frac{{\frac{1}{2}t + \frac{1}{2}}}{{t^2 - 1}} + \frac{{t^2 - 1}}{{t^2 - 1}}[/tex]")
![[tex]\frac{{t^2 - \frac{1}{2}t + \frac{1}{2}t + \frac{1}{2} + \frac{1}{2} - 1}}{{t^2 - 1}} = \frac{{t^2 }}{{t^2 - 1}}[/tex]](images/latex/a622ca7a785cb0f4a62dafbf2886ec52ecd53a74_0.png "[tex]\frac{{t^2 - \frac{1}{2}t + \frac{1}{2}t + \frac{1}{2} + \frac{1}{2} - 1}}{{t^2 - 1}} = \frac{{t^2 }}{{t^2 - 1}}[/tex]")
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