Question

(x+1)/(x-1)+(x+2)/(x-2)=(2x+13)/(x+1)

Answer 1

 

Answer 2

(x+1)/(x-1)+(x+2)/(x-2) = (2x+13)/(x+1) 

                         x ∈ R \{-1;1;2}

(x²-x-2+x²+x-2)/[(x-1)(x-2)] = (2x+13)/(x+1)

(2x²-4)/[(x-1)(x-2) = (2x+13)/(x+1)

2(x²-2)(x+1) = (2x+13)(x-1)(x-2)

2(x³+x²-2x-2) = (2x+13)(x²-3x+2)

2x³+2x²-4x-4 = 2x³-6x²+4x+13x²-39x+26

5x²-31x+30 = 0

Δ = b²-4ac = 961-600 = 361

√Δ = √361 = 19 

x1 = (-b-√Δ)/2a = (31-19)/10 = 12/10 = 6/5

x2 = (-b+√Δ)/2a = (31+19)/10 = 50/10 = 5

x = 6/5    v   x = 5