Compute  lim⁡ 𝑥→3⁡1𝑥-13𝑥-3

To compute the limit of the function as x approaches 3, we can use the limit laws. However, if we directly substitute x = 3 into the function, we get an indeterminate form (0/0). So, we need to simplify the function first.

The function is 1/(x - 1) - 3/(x - 3).

To simplify, we find a common denominator and combine the fractions:

= [(x - 3) - 3(x - 1)] / [(x - 1)(x - 3)]

= [x - 3 - 3x + 3] / [(x - 1)(x - 3)]

= [-2x] / [(x - 1)(x - 3)]

Now, we can substitute x = 3 into the simplified function:

lim (x->3) [-2x / (x - 1)(x - 3)] = -2*3 / [(3 - 1)(3 - 3)] = -6 / 0

This is undefined, so the limit does not exist.

To compute the limit of the function as x approaches 3, we can use the limit laws. However, if we directly