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

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

Jawaban Terkonfirmasi

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)

frac{1}{a+1} = frac{2-x}{3} …(1)
frac{2a +1}{ a^{2}-1 } = frac{4}{6x-3} …(2)
(1) + (2)
frac{-2 x^{2}+5x+2 }{6x-1}