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Express the following in partial fractions: (1+2x^2)/(3x-2)(x-1)^2

(1+2x^2)/(3x-2)(x-1)^2 = -5/x-1 + 3/(x-1)^2 + 17/3x-2
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Answered by Manny S. • Maths tutor
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let p be a polynomial p(x) = x^3+b*x^2+ c*x+24, where b and c are integers. Find a relation between b and c knowing that (x+2) divides p(x).

We know that (x+2) divides p(x), therefore p(x) can be written as p(x) = (x+2) q(x) + 0, where q is another polynomial of degree 2. We can calculate then p(-2): p(-2)= ((-2)+2) q(-2) = 0;p(-2)= (-2)^3+b (-2)...
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Answered by Tina-Alina S. • Maths tutor
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How would I solve a linear simultaneous equation?

When presented with a simultaneous equation, you need to find out the values of the letters (commonly x and y). You might be given two equations such as: a) 2x + 4y = 6, and b) -4x - 3y = 3. The first thing ...
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Answered by Ryan O. • Maths tutor
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Find the radius and centre of the circle given x^2+4x+y^2+2y=20

Complete the square:x 2 +4x gives (x+2) 2 -4y 2 +2y gives (y+1) 2 -1Therefore,(x+2) 2 -4+(y+1) 2 -1=20Rearranging gives:(x+2) 2 +(y+1) 2 =25Comparing to the standard equation for a circle:(x-a) 2 +(y-b) 2 =r...
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Answered by Stanley C. • Maths tutor
4761 Views

Solve the inequality x^2 – x < 6

The question is asking for the range of x values that satisfies the inequality. First rearrange the equation to form a quadratic: x 2 – x – 6 &lt; 0. Factorise the quadratic to find x-intercepts: ( x – 3 )( ...
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Answered by Lea L. • Maths tutor
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