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Split (3x-4)/(x+2)(x-3) into partial fractions

(3x-4)/(x+2)(x-3) = A/(x+2) + B/(x-3)=> 3x-4 = A(x-3) + B(x+2)Let x = -2-10 = -5AA = 2Let x = 35 = 5BB = 1∴ (3x-4)/(x+2)(x-3) = 2/(x+2) + 1/(x-3)

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A circle with centre C has equation x^2+8x+y^2-12y=12. The points P and Q lie on the circle. The origin is the midpoint of the chord PQ. Show that PQ has length nsqrt(3) , where n is an integer.

First complete the square for both x and y. Move all constants to the right hand side. The square root of this is the radius of the circle. The two constants in the completed square bracket show the x and...

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Integrate(1+x)/((1-x^2)(2x+1)) with respect to x.

To simplify the fraction first notice (1-x²) = (1-x)(1+x) so the common factor of (1+x) in the numerator and denominator can be cancelled. (1+x)/((1-x^2)(2x+1)) = 1/((1-x)(2x+1)), then we need ...

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