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Here, we are asked to differentiate with respect to x. That is what dy/dx stands for. So, we are only concerned with the terms involving x; that is x^3 and 2x. To differentiate you need to time x (and its...

So our first priority is to get all the Xs onto on side and add them together. But we cant do that just yet because of 3(x-2).

so lets move all X values to the left of the equation 3(x-2) + 2x <...

1/(x(1-3x))= A/x+ B/(1-3x) 1= A(1-3x) + B(1-3x)

when x=0    1=A

when x= 1/3     1=B/3 so B=3

1/(x(1-3x))= 1/x + 3/(1-3x)

9= 3² so 9^3x+1 = 3^2(3x+1) = 3^6x+2

y= 6x+2 where a=6 and b=2 

Firstly factorise the denominator to get (2x+7)(x+9). Then make the fraction equal to the seperate fractions with constants.

E.g 16x+78/2x^2+25x+63=A/(2x+7)+B/(x+9). then multiply accross by the de...