Practice Equations with algebraic fractions
A rational equation contains a variable in a denominator, so excluded values must be recorded before solving.
Check each candidate in the original equation.
Exercises with solutions
A fractional equation has the unknown in a denominator. First determine the domain: no denominator may become zero. Then multiply both sides by the common denominator and solve the resulting equation. Finally check that the solution lies in the domain.
Exercise 1
Solve 6/x = 3.
Show solution and working
x = 2
Multiply by x: 6 = 3x, so x = 2. Check: 6 ÷ 2 = 3.
Exercise 2
Solve 4/(x + 1) = 2.
Show solution and working
x = 1
Multiply by (x + 1): 4 = 2 · (x + 1), so 4 = 2x + 2 and x = 1. Domain: x ≠ −1.
Exercise 3
Which value may x not take in 5/(x − 3)?
Show solution and working
x = 3
At x = 3 the denominator becomes zero. Such values must be excluded from the domain.
Exercise 4
Solve 3/x + 1 = 4.
Show solution and working
x = 1
Rearrange first: 3/x = 3. Then multiply by x: 3 = 3x, so x = 1.
Common mistake
Forgetting the domain. Anyone who gets x = −1 from 4/(x + 1) = 2 has created a zero denominator; that solution must be discarded.
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