How do you solve #2/(x-1)+1=2/(x^2-x)#?
Configuring the equation so that both sides end up with the same denominator.
Consider just the left hand side
Putting it all together
As the denominators are the same on both sides the equation is equally true if you just equate the numerators to each other and totally forget about the denominators.
Let's simplify the left-hand side of the equation:
Then, let's cross-multiply:
We can expand the parentheses to get:
Let's move all terms to the left-hand side to form a cubic equation:
Now, let's factorise:
The difference of squares can be simplified to:
Therefore, the solutions to the equation are