Algebraic fractions add like number fractions: use a common denominator. For 4/(x + 1) + 2/(x + 3), the common denominator is (x + 1)(x + 3).
Multiply each numerator by the other denominator: 4(x + 3) + 2(x + 1) = 6x + 14. So the answer is (6x + 14)/((x + 1)(x + 3)). Factorise the top at the end in case anything cancels: here 2(3x + 7), with nothing to cancel.
Worked example
Write 1/(x + 1) − 3/(x − 3) as a single fraction.
- Numerator: (x − 3) − 3(x + 1) = x − 3 − 3x − 3.
- = −2x − 6 = −2(x + 3).
Answer:−2(x + 3)/((x + 1)(x − 3))
Key words
- common denominator
- a shared bottom expression
- single fraction
- one numerator over one denominator
- cancel
- divide out a common factor
Practise this
New questions every time.
Common Core-referenced: HSA-APR.D.6