How to solve this?

Question

10/(x^2-3x+5)=x+1

Answer 1

Clear the fraction. You can do this as long as
x^2 - 3x + 5 = 0
That is, x cannot be (3 +/- sqrt(29))/2

So, now we have

10 = (x+1)(x^2 - 3x + 5)
x^3 - 2x^2 + 2x - 5 = 0

Now get out your handy wolfram polynomial solver to find that x = 2.15