Lane went to the bookstore he spent 1/3 of his money on a pen and 4/6 of it on books what fraction of his money did he have left

First, you have to find a common denominator between 3 and 6. 3 goes into 6 evenly, so 6 is the lowest common denominator.( always go with the lowest common denominator.) Since 3 goes into 6 2 times, what you do to the denominator you do to the numerator.
1/3 x 2 = 2/6. 4/6 stays the same bc the denominator is already 6.
Now, 4/6 - 2/6 = 2/6
Lane had 2/6 of his money left.
Final 2/6

Sin(a)+cos(a)+cot(a)-1=2(csc(x)+1)