x = {√(a+1)+√(a-1)} / {√(a+1) - √(a-1)} find x
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Step-by-step explanation:
{√(a+1)+√(a-1)} / {√(a+1) - √(a-1)}
=[{√(a+1)+√(a-1)}{√(a+1)+√(a-1)} ]/ [{√(a+1) - √(a-1)}{√(a+1)+√(a-1)}] ,
multiplying by{√(a+1)+√(a-1)}/{√(a+1)+√(a-1)}
={√(a+1)+√(a-1)}^2 / [{√(a+1)}^2 - {√(a-1)}^2]
={√(a+1)+√(a-1)}^2 / [(a+1) - (a-1)]
={√(a+1)+√(a-1)}^2 / [1+1]
=[{√(a+1)}^2 + 2√(a+1)(a-1)+{√(a-1)}^2]/2
={a+1 +2√(a^2-1)+a-1}/2
={2a+2√(a^2-1)}/2
=a+√(a^2-1)
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