- Difficulty
- Standard
- Suggested time
- 3 min
- Marks
- 2
Functions, graphs and inverses practice question 15
Which expression equals the one below wherever both are defined?
Factor the top and the bottom completely, then cancel a factor they share.
is a difference of squares. For , find two numbers that multiply to and add to .
Theory UBC Math 100 §1.5CLP-1 §0.5Key results
Worked solution
Strategy
Only whole factors cancel, so factor both quadratics first and then divide out the factor they share. The result agrees with the original wherever both are defined.
Working
A difference of squares, and a quadratic whose roots are 3 and −2.
Divide out the shared factor x − 3. The two agree at every x except 3 and −2, where the original is undefined.
Answer
The answer is x plus 3 over x plus 2.
Check
At x = 1 the original is (1 − 9)/(1 − 1 − 6) = 8/6 = 4/3, and (1 + 3)/(1 + 2) = 4/3.
Where this goes wrong
Cancelling the x² terms, or a sign slip in factoring x² − x − 6. Only whole factors cancel, and the factors of x² − x − 6 multiply to −6 and add to −1.
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