Rational Expressions and Equations

Simplifying with non-permissible values stated, operations, and solving rational equations with extraneous roots.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

Simplify (x² − 9)/(x² + 5x + 6), stating the non-permissible values.
What are the non-permissible values of (x + 1)/(x² − 4x)?
Solve 6/x = 2/(x − 4).
Simplify x/(x + 2) + 3/(x + 2).
Solve x/(x − 3) − 2 = 3/(x − 3).
Solve x + 6/x = 5. What is the greater solution?
Simplify 2x/(x² − 1) ÷ x/(x + 1), stating the non-permissible values.
Pipe A fills a tank in 6 hours and pipe B fills it in 3 hours. How many hours do they take together?
Solve 5/(x − 2) = (x + 1)/(x − 2).
A boat goes 18 km downstream and 18 km back. Its speed in still water is 12 km/h and the round trip takes 3.2 hours. What is the speed of the current, in kilometres per hour?