Bagaimana Anda menyederhanakan (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)), a> 1?

Bagaimana Anda menyederhanakan (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)), a> 1?
Anonim

Menjawab:

Pemformatan matematika besar …

Penjelasan:

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

# = warna (merah) (((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1)))) / (sqrt (a + 1) / (sqrt (a-1) cdot sqrt (a-1) cdot sqrt (a + 1) -sqrt (a + 1) cdot sqrt (a + 1) sqrt (a-1))) #

# = warna (biru) (((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1)))) / (sqrt (a + 1) / (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) #

# = warna (merah) ((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1))) xx (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) / sqrt (a + 1) #

# = warna (biru) ((1 / sqrt (a-1) + sqrt (a + 1)) xx ((sqrt (a + 1) cdot sqrt (a-1)) / (sqrt (a-1) - sqrt (a + 1))) xx (batal ((sqrt (a + 1))) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) / cancelsqrt (a + 1)) #

# = warna (merah) (((1 + sqrt (a + 1) cdot sqrt (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) -sqrt (a + 1)) #

# = warna (biru) (((1 + sqrt (a + 1) cdot sqrt (a-1)) / batal (sqrt (a-1))) xx ((sqrt (a + 1) cdot cancel ((sqrt (a-1)))) / warna (merah) (batal (warna (hijau) ((sqrt (a-1) -sqrt (a + 1))))) xx sqrt (a-1) warna cdot (merah) (batalkan warna (hijau) ((sqrt (a-1) -sqrt (a + 1))) #

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

Menjawab:

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

Penjelasan:

Untuk menyederhanakan banyak hal yang akan kita gunakan # u ^ 2 = a + 1 # dan # v ^ 2 = a-1 #, yang memberi kita:

# (v ^ -1 + u) / (u ^ -1-v ^ -1) * (uv ^ 2-vu ^ 2) / u = ((v ^ -1 + u) (uv ^ 2-vu ^ 2)) / (u (u ^ -1-v ^ -1)) = (uv-u ^ 2 + (uv) ^ 2-vu ^ 3) / (1-uv ^ -1) = (uv (1 + uv) -u ^ 2 (1 + uv)) / ((vu) / v) = (uv (1 + uv) (vu)) / (vu) = uv (1 + uv) #

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