Can YOU Solve This Rational Equation in 10 Minutes?

[@RashmiRay-c1y]

Let y=3x^2-2. Then, 2x/(y-x) +3x/(2y+x) = 1 which yields y(y-4x)=0. If y=0, x = +/-√(2/3). If y=4x, 3x^2-4x-2 =0 and x = 1/3[2 +/-√10]. Thus, x=+/-√(2/3), 1/3[2 +/-√10].

[@backgammonmaster]

Precisely as I solved it in about 2 minutes. it simplifies beautifully , no need for all that heavy machinery !🙂

[@RealQinnMalloryu4]

1x/1x^1 ➖ x ➖ 1+3x/3^3x^2+x ➖ 2^2 1x/3^1x^1 +x ➖ 1^2 /3^1x+x ➖ 1^2 /3x+x ➖ 2 (x ➖ 3x+2).

[@Fjfurufjdfjd]

Πρεπει οι παρονομαστες διαφοροι του 0.
Θετω 3χ^2-χ-2=ψ (ψ=/0)
Τοτε εχω: 6χ^2-2χ-4=2ψ
6χ^2-4+χ=2ψ+3χ
6χ^2+χ-4=2ψ+3χ. Η εξισωση γινεται
2χ/ψ + 3χ/(2ψ+3χ)=1 ψ=/-(3χ)/2
2χ(2ψ+3χ)+3χψ=ψ(2ψ+3χ)
4χψ+6χ^2+3χψ=2ψ^2+3χψ
4χψ+6χ^2=2ψ^2
2χψ+3χ^2=ψ^2
Ψ^2-2χψ=3χ^2 ; ψ^2-2χψ+χ^2=4χ^2
(ψ-χ)^2=(2χ)^2
(ψ-χ-2χ)(ψ-χ+2χ)=0
ψ=3χ ή ψ=-χ ; 3χ^2-χ-2=3χ ή 3χ^2-χ-2=-χ
3χ^2-4χ-2=0 ή 3χ^2=2
χ=[2+-(10)^(1/2)]/3 ή χ=+-(6)^(1/2)/3 δεκτες
Πρεπει χ=/1 ; -2/3 ; [-1+-(97)^(1/2)]/12.

[@Fjfurufjdfjd]