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Homework Statement
If lim as X approaches 2 of [f(x)-5]/(x-2)=3, find the lim as x approaches 2 of f(x)
Homework Equations
The Attempt at a Solution
This is how I solved:
If lim as X approaches 2 of [f(x)-5]/(x-2)=3, then:
([lim as X approaches 2 f(x)]-5)/(2-2)=3
= ([lim as X approaches 2 f(x)]-5)/0=3
Multiplying through by 0, I got
[lim as X approaches 2 f(x)]-5=0,
or, the lim as x approach 2 of f(x)=5.
This is the answer given in the back of the book as well. My question is, is the step where I multiplied a zero denominator through both sides valid? If you can do that, is there any underlying logic? If you can't, what is the correct way to solve this problem? Thank you.