Question 463912
23/(x-1) + 3 - 70/(x^2-4x+3) = 0
...
23/(x-1) + 3 - 70/(x^2-4x+3) = 0
23/(x-1) + 3 - 70/(x-1)(x-3) = 0
LCD:(x-1)(x-3)
multiply each term by the LCD, getting rid of the fractions.
23(x-3)+3(x-1)(x-3)-70=0
23(x-3)+3(x^2-4x+3)-70=0
23x-69+3x^2-12x+9-70=0
3x^2+11x-130=0
solve by following quadratic formula:
..
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
..
a=3, b=11, c=-130
x=[-11ħsqrt(11^2-4*3*-130)]/2*3
x=[-11ħsqrt(121+1560)]6
x=[-11ħ√1681]/6
x=[-11ħ41]/6
x=30/6=5
or
x=52/6