당신은 어떻게 단순화합니까 (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a + 1) / ( (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)

대답:

거대한 수학 포맷 …

설명:

#color (청색) (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a- +1) / ((a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)))

(a + 1) - (sqrt (a + 1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1) -sqrt (a + 1) cdot sqrt (a-1) cdot sqrt (a-1) a + 1) sqrt (a-1)))

(a + 1) - (sqrt (a + 1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1)) / sqrt (a + 1) / (sqrt (a + 1)

(a + 1) - (sqrt (a + 1)) / (sqrt (a + 1)) sqrt (a-1))) / sqrt (a + 1) # (sqrt (a-1)

(a + 1) - (sqrt (a + 1) - (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) / cancelsqrt (a + 1))) #

(a-1)) / (sqrt (a-1))) xx ((sqrt (a + 1) cdot sqrt (a-1))) / (sqrt (a-1) -sqrt (a + 1))) xx sqrt (a-1) cdot (sqrt (a-1)

(a + 1) cdot 취소 ((sqrt (a-1))) xx ((sqrt (a + 1) cdot 취소 (a-1))))))) / 색상 (적색) (취소 (색상 (녹색) ((sqrt (a-1) -sqrt (a + 1)))))) xx sqrt (a-) (취소 색 (녹색) ((sqrt (a-1) -sqrt (a + 1))) #

(a + 1) cdot (sqrt ((a + 1) (a-1))) = (적색) (ul (bar (| color (blue)) | #

대답:

#sqrt (a ^ 2-1) + a ^ 2-1 #

설명:

크게 단순화하기 위해 우리는 # u ^ 2 = a + 1 # 과 # v ^ 2 = a-1 #, 그것은 우리에게 준다:

(v ^ -1 + u) / (u ^ -1-v ^ -1) * (uv ^ 2-vu ^ 2) / u = 1) = (uv-u-2) / (uv-1) (1 + uv)) / (vu) / (vu) = uv (1 + uv)

(a + 1) + (a + 1) = sqrt (a ^ 2-1) + a (1 + uv) = uv + u ^ 2v ^ 2 = sqrt ^ 2-1 #