Hvordan forenkler du (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)), a> 1?

Svar:

Stor matematikkformatering …

Forklaring:

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

# = Farger (rød) (((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 et + 1) sqrt (a-1))) #

# = Farge (blå) (((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)

# (f) (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)

# = farge (blå) (1 / sqrt (a-1) + sqrt (a + 1)) xx ((sqrt (a + 1) cdot sqrt (a-1)) / sqrt (a + 1))) xx (avbryt ((sqrt (a + 1))) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1))) / cancelsqrt)) #

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

# = farge (blå) ((1 + sqrt (a + 1) cdot sqrt (a-1)) / avbryt (sqrt (a-1))) xx ((sqrt (a + 1) cdot avbryt (a-1)))) / farge (rød) (avbryt (farge (grønn) (sqrt (a-1) -sqrt (a + 1)))) xx sqrt (a-1) cdotfarge) (Avbryt farge (grønn) ((sqrt (a-1) -sqrt (a + 1)))

# (1 + sqrt (a + 1) cdot sqrt (a-1)) cdot (sqrt (a + 1) (a-1)))) | #

Svar:

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

Forklaring:

For å forenkle ting vi sterkt vil bruke # U ^ 2 = a + 1 # og # V ^ 2 = en-1 #, som gir oss:

# (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 #