Explain one identity 3(/x-1 -2/x+1 ):x+2/x^2-1=2 Solution You need to establish the identity [(3/(x-1) -2/(x+1)):(x+2)/(x^2-1)=2. ] Notice that you need to multiply brackets by reverse of fraction [(x+2)/(x^2-1)] such that: [(3/(x-1) -2/(x+1))*(x^2 -1)/(x+2) = 2] You need to bring the fractions in brackets to a common denominator such that: [((3(x+1)-2(x-1))/(x-1)(x+1))*(x^2 -1)/(x+2) = 2] Notice that you may write the common denominator as difference of squares such that: [((3(x+1)-2(x-1))/(x^2 - 1))*(x^2 -1)/(x+2) = 2] Reducing by ( [x^2 - 1] ) yields: [(3(x+1)-2(x-1))/(x+2) = 2] You need to open the brackets to numerator such that: [(3x + 3 - 2x + 2)/(x + 2) = 2] [(x+5)/(x+2)=2 =gt x + 5 = 2x + 4] The last line proves that the identity is not established..

1. Explain percentiles and give an example of how it is used in statistics
Solution
Percentiles, is to put simply just percentages. To be in the 90th percentile, refers to
being at 90%. But it depends on how you say it. One of the easiest way to understand this is
grades. In school everyone gets grades. How well you do is then ranked among all the other
students. So say you took a few tests and you ranked in the top 10 percentile. That means your
grades are in the top 10% of the class. If you say you are ranked in the 90th percentile, that
means you are at the 90% of the class. Meaning you are doing better than 90% of all the other
students, but there may be upwards of 10% of students doing better than you.