Solve the equation for x and show all work

(x

^{2}+2)/(3x^{2}-5x+2)+-3/(x-1)=-5/(3x-2)-
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Solve the equation for x and show all work

(x^{2}+2)/(3x^{2}-5x+2)+-3/(x-1)=-5/(3x-2)

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(x^2+2)/(3x^2-5x+2)+(-3)/(x-1)=-5/(3x-2)

x can't be equal to 1 and x can't be equal to 2/3 (each will make one or more denominators 0.)

(x^2+2)/(3x-2)(x-1)+(-3)/(x-1)=-5/(3x-2)

a common denominator is (3x-2)(x-1)

(x^2+2)/(3x-2)(x-1)+(-3)(3x-2)/(3x-2)(x-1)=-5(x-1)/(3x-2)(x-1)

[x^2+2+(-3)(3x-2)]/(3x-2)(x-1)=-5(x-1)/(3x-2)(x-1)

x^2+2-9x+6=-5x+5

x^2+2-9x+6+5x-5=0

x^2-4x+3=0

(x-3)(x-1)=0

x-3=0 and x-1=0

x=3 and x=1(in the beginning we said x cannot be 1)

x=3 is the only solution

check: (3^2+2)/(3*3^2-5*3+2)+(-3)/(3-1)=-5/(3*3-2)

11/14+(-3/2)=-5/7

11/14+(-21/14)=-5/7

-10/14=-5/7

-5/7=-5/7

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