Partial fractions and rational functions

Question 1 of 10

A proper fraction is one in which

Question 2 of 10

Partial fractions are useful for integration.

Question 3 of 10

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

Question 4 of 10

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

Question 5 of 10

Express (2x + 3)/(x + 1)² in partial fractions.

Question 6 of 10

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

Question 7 of 10

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

Question 8 of 10

1/[x(x + 4)] = (1/4)[1/x − 1/(x + 4)]. The value of the constant outside the brackets is 1/___

Question 9 of 10

1/[x(x + 5)] = (1/5)[1/x − 1/(x + 5)]. The value of the constant outside the brackets is 1/___

Question 10 of 10

The denominator (x² + 1) factorises into real linear factors.