Jika a = (x+1)/(2-x) maka 1/(a+1) + (2a+1)/(a^2-1) sama dengan

1/(a + 1) + (2a + 1)/(a² - 1)
= ((a - 1) + (2a + 1)) / (a² - 1)
= (3a)/(a² - 1)
substitusi:
3((x + 1)/(2 - x)) / (((x + 1)/(2 - x))² - 1)
= [(3x + 3)/(2 - x) ] / ((x² + 2x + 1 - (4 - 4x + x²)) / (2 - x)²)
= [(3x + 3)(2 - x)](2 - x)² / (6x - 3)

[tex] \frac{1}{a+1} = \frac{2-x}{3} [/tex] ...(1)
[tex] \frac{2a +1}{ a^{2}-1 } = \frac{4}{6x-3} [/tex]...(2)
(1) + (2)
[tex] \frac{-2 x^{2}+5x+2 }{6x-1} [/tex]