Left-handed limit of a rational function

Homework Statement

What is Lim (1+x2)/(4-x) as x approaches 4 from the left? Prove using the definition.

The Attempt at a Solution

Well x≠4. Function approaches positive infinity as x approaches 4 from the left side. Let m>0 and 0<x<4.
Then (1+x2)/(4-x) > x2/(4-x) > x/(4-x) > m when x...here I am stuck.
So basically I need to show that if x>xm then (1+x2)/(4-x) >m?
But at some point the same function approaches negative infinity so do a choose xm=(something, 4)?

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PeroK
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Homework Statement

What is Lim (1+x2)/(4-x) as x approaches 4 from the left? Prove using the definition.

The Attempt at a Solution

Well x≠4. Function approaches positive infinity as x approaches 4 from the left side. Let m>0 and 0<x<4.
Then (1+x2)/(4-x) > x2/(4-x) > x/(4-x) > m when x...here I am stuck.
So basically I need to show that if x>xm then (1+x2)/(4-x) >m?
But at some point the same function approaches negative infinity so do a choose xm=(something, 4)

It's usually a good idea to simlify things as much as possible before you start.

What can you say about ##1+x^2## and ##1##?

Svein