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log_{x} (7y+1) - log{x} (2y) =1 --> log_{x} [(7y+1)/2y]=1 (y =/= 0, Rules of logarithms i.e. difference of logarithms) --> x = [(7y+1)/2y] (x>0, Rules of logarithms i.e. log_{x} x = 1) --> 2yx...

A/(x-2) + B/(x+1) + C/(x+1)^2

First, we start by moving the x's all over to one side. These are our undefined variable and it is important to keep them together. To do this, we take away 3x from either side and we get:

3x - 3 &...

The interior angle of a regular shape is the angle found on the inside of the shape at each of its corners. A twelve-sided regular polygon is too complex to remember its geometric rules so we must divide ...

if y=3x^2 + x -4 

then 

dy/dx = 6x + 1

setting this equal to zero gives

6x + 1 = 0

so then

x = -1/6

putting this x value back into the original equation gi...