How do you solve #ln ( x - 1) + ln x - ln ( x^2 + x - 2 ) = 0#?
Use the rule which states that the sum of two logarithms is the logarithm of the product, and that the difference of two logarithm is the logarithm of the ratio.
For the first rule, you have that
For the second rule, you have that
This expression can be further simplified, since the solutions of
And so the final answer is