The question is in regards to this equation:
- $$\left(\frac{\sqrt3+1}{1+\sqrt3+\sqrt{t}}+\frac{\sqrt3-1}{1-\sqrt3+\sqrt{t}}\right)\cdot\left(\sqrt{t}-\frac{2}{\sqrt{t}+2}\right)$$
From what I have from trying to simplify is the following:
- $$\frac{(\sqrt3+1)(1-\sqrt3+\sqrt{t})+(\sqrt3-1)(1+\sqrt3+\sqrt{t})}{(1+\sqrt3+\sqrt{t})(1-\sqrt3+\sqrt{t})}\left(\frac{\sqrt{t}(\sqrt{t}+2)-2}{\sqrt{t}+2}\right)$$
expanded; it simplifies to:
- $$\frac{2\sqrt{3t}}{-2+2\sqrt{t}+t}\cdot\frac{t+2\sqrt{t}-2}{\sqrt{t}+2}$$
then $${-2+2\sqrt{t}+t}$$ cancels, leaving:
my answer to be:
- $$\frac{2\sqrt{3t}}{\sqrt{t}+2}$$
But the answer, according to my teacher, is $$t=4.$$
My question is how?
I have tried to multiply my answer by the conjugate but to no avail. Do you have any tips or tricks to help me?
Thank you!!