See if you can simplify the (1/m -1/4)/(m-4).Originally Posted bycinder

= [(4 -m)/4m] / (m-4)

See those (4-m) and (m-4), they are the same but one is the negative of the other. If they are exactly the same, then they will cancel each other. So we make them exactly the same.

Say, we turn (4-m) into (m-4). The step is one of the simplest switch in Math. (4-m) becomes -(m-4). One way it's done is by multiplying the (4-m) by (-1 / -1), which is actually 1.

(4-m)*(-1 / -1) = (-4 +m) / -1 = -(-4 +m) = -(m-4). Easy.

So,

[(4-m)/4m] / (m-4)

= [-(m-4)/4m] / (m-4)

= -1/(4m)

Therefore,

Limit(m-->4) [(1/m -1/4)/(m-4)]

= Limit(m->4) [-1/(4m)]

= -1/(4*4)

= -1/16 -------------answer.