[tex] \frac{3}{x^2-7x+10}+2= \frac{x-4}{x-5} [/tex]
if we factor (x²-7x+10) we get (x-5)(x-2)
multiply bot sides by (x-5)(x-2)
3=(x-4)(x-2)
3=x²-6x+8
minus 3 both sides
0=x²-6x+5
what 2 numbers multily to 5 and add to -6?
-5 and -1
0=(x-1)(x-5)
set to zero
x-1=0
x=1
x-5=0
x=5
x=1 and 5
