Partial fractions and rational functions

Question 1 of 10

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

Question 2 of 10

A proper fraction is one in which

Question 3 of 10

Express (2x + 8)/[(x + 2)(x + 4)] in partial fractions. Find the value of B in A/(x + 2) + B/(x + 4).

Question 4 of 10

Express (x² + 1)/[(x − 1)(x + 1)] in the form A + B/(x − 1) + C/(x + 1).

Question 5 of 10

An improper fraction can be decomposed directly without division.

Question 6 of 10

The partial fractions of 1/[(x − 1)(x − 2)] have the form

Question 7 of 10

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

Question 8 of 10

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

Question 9 of 10

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

Question 10 of 10

Express (5x + 1)/[(x − 1)(x + 2)] in partial fractions.