how can we solve this for x:(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a

Ok there are two way to proceed for this
one is to actually take the LCM and solve all the complicated equations and in the end you will get something like this


which give two roots as
0 and a+b

Second you can easily observe that zero is definitely one root and the equation is a quadratic, so just compute first two coefficient and get the sum of roots which will be the second root