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Express the following in partial fractions: (x^2+4x+10)/(x+3)(x+4)(x+5)

(x^2+4x+10)/(x+3)(x+4)(x+1) = A/(x+3) + B/(x+4) + C/(x+1) [A(x+4)(x+1) + B(x+3)(x+1) + C(x+3)(x+4)]/(x+3)(x+4)(x+1) = (x^2+4x+10)/(x+3)(x+4)(x+1) [A(x+4)(x+1) + B(x+3)(x+1) + C(x+3)(x+4)] = (x^2+4x+10) A(...

Answered by Alessandro S. • Maths tutor

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Curve D has equation 3x^2+2xy-2y^2+4=0 Find the equation of the tangent at point (2,4) and give your answer in the form ax+by+c=0, were a,b and c are integers.

Differentiate the equationdy/dx=6x+2x(dy/dx)+2y-4y(dy/dx)Set this equal to zero and solve for dy/dx which gives:dy/dx=(2y+6x)/(4y-2x)For x=2 and y=4 dy/dx=5/3(y-y_o)=m(x-x_o)y-4=(5/3)(...

Answered by Vasileios D. • Maths tutor

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Integrate 3x^2 + 4/3 x^5 with respect to x

3x³ /3 + 4x⁶/(6x3) = x³ + 2x⁶/9 + c

Answered by Ellis B. • Maths tutor

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How do you integrate a fraction when x is on the numerator and denominator?

Firstly, ensure both numerator and denominator are factorised fully so that any possible cancellations can happen - making it easy for yourself is always a good idea. Now, turn it into partial fractions. ...

Answered by Jack W. • Maths tutor

6236 Views

integrate (2x)/(x^2+1) dx with limits 1, 0

Firstly we notice that the numerator is the derivative of the denominator so we can use integration by subsitution method. Setting u=x^(2)+1. We can differentiate this to get du/dx=2x Subbing in dx=du/2x ...

Answered by Tanya J. • Maths tutor

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