Rationalize \( \frac{\sqrt{1+x}+\sqrt{x}}{\sqrt{1+x}-\sqrt{x}} \)

4. Two almirahs are purchased for \( 27,800 . ₹ 200 \) was spent on the transportation. One of them is sold at a profit of \( 40 \% \) and the other one at a loss of \( 40 \% \). If the selling price was same in both the cases, find the cost price of each alminh?

6) \( \frac{3 a^{-2}-4 b^{-1}+a b}{3 a b-2 a} \quad a=3 ; b=4 \)

83 Olivia drove 170 miles each way (there and back) to visit her cousin. On the trip, Olivia drove an extra 20 miles to see the Grand Canyon. She also drove an extra 45 miles to see Lake Powell. Write one or more equations you could use to represent the total number of miles Olivia drove on her trip. Show your work.

\( A^{-1}=\frac{1}{\operatorname{det} A}(\operatorname{adj} A) \)

8 Olivia drove 170 miles each way (there and back) to visit her cousin. On the trip, Olivia drove an extra 20 miles to see the Grand Canyon. She also drove an extra 45 miles to see Lake Powell. Write one or more equations you could use to represent th number of miles Olivia drove on her trip.