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Start by multiplying equation (2) by 4 so both equations contain 4 lots of x: 4x - 12y = 20 Then take away equation 1 from equation 2 to eliminate x -13y = 13 divide by 13 and then reverse the negative si...

To solve this you need to integrate by substitution. You can spot this because the differential of the bottom of the fraction is a multiple of the top part, showing this quickly; if u = x²  + 3...

The equation we use to integrate by parts is

y = uv - ∫ v(du/dx) dx + c

so we separate dy/dx into u=(3x-4) and dv/dx=(2x²+5)

however we still need to find du/dx an...

de Moivre worked out a brilliant and beautiful way to solve complex equations.

If you for example have z³= 1 and you want to find all real and complex z that satisfy thi...

expand the brackets to get x²-2x+3x-6=4x+22 bring all the terms to one side x²-2x+3x-6-4x-22=0 (remember:if you do something to one side, do the same thing to the other! e.g. -4x on ...