First, multiply by the conjugate of 1-x, which is 1−x21+x.
Then, simplifying things, we get limx→1(−xlnxx−1).
Which then turns into this: −limx→1(1−1+xln(x)1x)limx→1(1−1+xln(x))limx→1(1x)
Using L'Hopital's rule and simplifying, we get that this equation is equal to 1.
We also need to find the value of limx→1(1x) which is easily equal to 1.
Therefore your answer is −11=−1.