Elective Mathematics

1Express (3x + 4)/[(x + 4)(x + 5)] in partial fractions. Find the value of B in A/(x + 4) + B/(x + 5).

2Express (4x + 1)/[(x + 5)(x + 4)] in partial fractions. Find the value of B in A/(x + 5) + B/(x + 4).

31/[x(x + 1)] = (1/1)[1/x − 1/(x + 1)]. The value of the constant outside the brackets is 1/___

4Before using partial fractions on an improper fraction one should

5Express (4x + 7)/[(x + 2)(x + 3)] in partial fractions. Find the value of A in A/(x + 2) + B/(x + 3).

6Partial fractions are useful for integration.

7Express (2x + 2)/[(x + 3)(x + 1)] in partial fractions. Find the value of B in A/(x + 3) + B/(x + 1).

81/[x(x + 6)] = (1/6)[1/x − 1/(x + 6)]. The value of the constant outside the brackets is 1/___

91/[x(x + 2)] = (1/2)[1/x − 1/(x + 2)]. The value of the constant outside the brackets is 1/___

101/[x(x + 3)] = (1/3)[1/x − 1/(x + 3)]. The value of the constant outside the brackets is 1/___