The first step is to factor the denominators
#5/(x^2-6x+8)-2/(x^2+3x-10) = 8/(x^2+x-20)#
#color(red)(5/((x-4)(x-2))) -color(blue)(2/((x+5)(x-2))) = color(green)(8/((x+5)(x-4)))#
In an equation with fractions we can get rid of the denominators by multiplying each term by the LCM.
In this case it is #color(brown)((x-4)(x-2)(x+5))#
Taking one term at a time gives the following:
#color(red)(5/(cancel(x-4)cancel(x-2))) xx color(brown)(cancel(x-4)cancel(x-2)(x+5)) = 5(x+5)#
#color(blue)(2/(cancel(x+5)cancel(x-2))) xx color(brown)((x-4)cancel(x-2)cancel(x+5)) = 2(x-4)#
#color(green)(8/(cancel(x+5)cancel(x-4))) xx color(brown)(cancel(x-4)(x-2)cancel(x+5)) = 8(x-2)#
Simplifying each term leaves us with:
#5(x+5)-2(x-4) = 8(x-2)#
#5x+25 -2x+8 =8x-16#
#25+8+16 = 8x -5x +2x#
#49 = 5x#
#x = 49/5#
