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factorise the top fraction: 3x^2 - x - 2 = (3x + 2)(x - 1)

factorise the bottom fraction: x^2 -1 = (x + 1)(x - 1)

cancel out the (x - 1) and the final result is (3x + 2) / (x + 1)

First, you must remember what the midpoint formula is for a line with two points.

M= ((x_1​+x_2​)/2 ​,(y₁​+y_2​​)/2)

Then apply it to this question.<...

to find the area integrate the function between 0 and pi/2:

indefinite integral of y = -1/2 cos(2x) + sin(x) + c

ignore c and input boundary conditions:

[-1/2 cos(pi) + sin(pi/2)] - [...

rewrite as y = 4x^5 - 5x^(-2)

dy/dx = 20x^4 + 10x^(-3)

integral of y = 4x^6 / 6 + 5x^(-1) / 1 + c

simplify: 2/3 x^6 + 5/x

The first step would be to consider each of the powers individually, work out their value and then proceed with the subtraction to end up with a result. Firstly, as this question is to be done without a c...