Paano mo pinasimple (1 - x ^ 2) ^ (1/2) - x ^ 2 (1 - x ^ 2) ^ (- 3/2)?

Sagot:

# ((- x ^ 2 + x + 1) (- x ^ 2-x + 1)) / (1-x ^ 2) ^ (3/2) #

Paliwanag:

# (1-x ^ 2) ^ (1/2) -x ^ 2 (1-x ^ 2) ^ (- 3/2) #

Gagamitin natin: #color (pula) (a ^ (- n) = 1 / a ^ n) #

# <=> (1-x ^ 2) ^ (1/2) -x ^ 2 / (1-x ^ 2) ^ (kulay (pula) (+ 3/2)) #

Gusto namin ng dalawang fractions na may parehong denamineytor.

(1-x ^ 2) ^ (1/2) * kulay (berde) ((1-x ^ 2) ^ (3/2))) / kulay (green) ((1-x ^ 2) ^ (3/2)) - x ^ 2 / (1-x ^ 2) ^ (+ 3/2) #

Gagamitin natin: #color (pula) (u ^ (a) * u ^ (b) = u ^ (a + b)) #

# <=> (kulay (pula) ((1-x ^ 2) ^ (2))) / (1-x ^ 2) ^ (3/2) -x ^ 2 / (1-x ^ 2) ^ (3/2) #

# <=> ((1-x ^ 2) ^ (2) -x ^ 2) / (1-x ^ 2) ^ (3/2) #

Gagamitin namin ang sumusunod na pagkakakilanlang polinomyal:

#color (asul) ((a + b) (a-b) = a ^ 2-b ^ 2) #

# <=> kulay (asul) ((1-x ^ 2 + x) (1-x ^ 2-x)) / (1-x ^ 2) ^ (3/2) #

# <=> ((-x ^ 2 + x + 1) (- x ^ 2-x + 1)) / (1-x ^ 2) ^ (3/2) #

Hindi namin maaaring gawin mas mahusay kaysa sa ito, at ngayon maaari mong madaling (kung gusto mo) hanapin ang solusyon ng # ((-x ^ 2 + x + 1) (- x ^ 2-x + 1)) / (1-x ^ 2) ^ (3/2) = 0 #