Cancelling a factor that can be zero
Cancelling a factor that can be zero
IP 2
6 marks
A student solves \(\dfrac{x^2-4}{x-2}=4\) as follows: "Cancel to get \(x+2=4\), so \(x=2\)."
- Explain the error in the student's working and state the correct solution of the equation.[3]
- Find all values of \(k\) for which the equation \(\dfrac{x^2-4}{x-2}=k\) has no solution.[3]
Solution:
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Answer:(a) \(x=2\) makes the denominator zero, so it is not allowed; no solution (b) \(k=4\)
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