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How do I break down (x-2)/((x+1)(x-1)^2) into partial fractions?

Firstly, let (x-2)/((x +1)(x-1) 2 ) = A/(x+1) + B/(x-1)+C/(x-1) 2 , where A,B and C are to be calculated. Then, multiply both sides of the equation by (x+1)(x-1) 2 which will leave an equation as follows; x-...
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Answered by Daniel O. • Maths tutor
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A curve C has the equation x^3 + 2xy- x - y^3 -20 = 0. Find dy/dx in terms of x and y.

Every term needs to be differentiated in terms of x: For the x 3 term , differentiated it becomes 3x 2 (multiply the whole term by the initial power, 3, and the reduce the power by 1 and replace it, 3 theref...
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Answered by Seb T. • Maths tutor
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Why is the derivative of a function its gradient?

So, the easiest way to start thinking about this is by looking at straight lines. The gradient of a straight line is just its slope, which is the difference in the y values between any two points, divided by...
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Answered by Connor G. • Maths tutor
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integrate x^2 + 3x + 4

For the x 2 term we add one to the power, and then divide by 3 to get x 3 /3 For the next term we add one to the power and divide by the new power to get 3x 2 /2 We do the same for the 4, which just goes to ...
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Answered by Harry B. • Maths tutor
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Given that the curve y = 3x^2 + 6x^1/3 + (2x^3)/3x^1, find an expression for the gradient of the curve.

To find the gradient of a curve, you simply differentiate the equation of the curve. The first thing I like to do in any differentiation question is to simplify each expression where you can i.e. whenever th...
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