Xsq - 5 + 2 = 2
___________

Xsq - 5X + 3

HINT: Let Y = Xsq - 5X + 2
Therefore Y + 1 = Xsq - 5X + 3

Answer X = 4,8 or X = 0,2 or X = 1 or X = 4

After a brief introduction to solving quadratic equations, the above
problem is posed, which defies step-by-step solution. Any help would be kindly appreciated. Many thanks.

2. This is quite simple:

We have $(x^2-5x+2)/(x^2-5x+3)=2$

Rearranging, we get:
$
x^2-5x+2=2x^2-10x+6$

Bringing the terms over to the left we get:

$-x^2+5x-4=0$

Multiply through by -1 and factorise:

$x^2-5x+4=(x-1)(x-4)=0$

Hence x=1 or 4

3. If you have a quadratic that is not easily factored, or your teacher asks you to do the "quadratic method", use this method here: