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3x²+11x-4=0 #Factorise to find where the curve crosses the x axis (3x-1)(x+4)=0 #Each bracket equals 0 x=1/3, -4  #Integrate the curve between these two points to find the area enclosed in the ...

(x - 5) / (x² + 2x - 15) 

Let k(x) = f(x)g(x) then k'(x) = limit as h --> 0 of: (h(x+h)-h(x))/h = lim (f(x+h)g(x+h) - f(x)g(x))/h

We can factorise the numerator as:
f(x+h)g(x+h) - f(x)g(x) =f(x+h)g(x+h) -g(x)...

32x + 7

Answer: 16x/(x - 2)

Start with the numerator of the first fraction, 16x² + 4x³ , take a factor of 4x² out to get 4x²(4 + x). Then look at the denominator...