50 PTS JUST CHECK MY WORK
5x/2x-3 + -4x^2/3x+1
5x(3x+1)/2x-1(3x+1) + -4x^2(2x-3)/3x+1(2x-3)
foil each one
15x^2+5x-8x^3+12x^2/(2x-3)(3x+1)
simplify
-8x^3+27x^2+5x/(2x-3)(3x+10)
factor out an x
x(8x^2+3x+5)/(2x-3)(3x+10)
excluded values:
2x-3=0 3x+10=0
+3 +3 -10 -10
2x=3 3x=-10
/2 /2 /3 /3
x cannot=3/2 or -10/3
