Question

Se a= 1 sobre 1+X e b=1 -X com
X>1 então a+b sobre a-b é igual a ??

Answer 1

a= 1/(1+x)   e  b = 1 - x

a + b = 1/(1+x)+(1-x) = [ 1 + (1+x)·(1-x)] / (1+x) =[1+(1²-x²)] / (1+x) =[1+1-x²] / (1+x)=  (2 - x²) / (1+x)

a - b = 1/(1+x) - ( 1-x)= [1-(1-x)·(1+x) ] / (1+x) =[1-(1²-x²)] / (1+x) =
[ 1 - 1 + x²] / (1+x) = x² / (1+x)

(a+b) / (a- b) =[ (2 - x²) / (1+x)] / [ x² / (1+x) ] =
[ (2 - x²) / (1+x)] ·[ (1+x) / x² ] = ( 2 - x²) / x²

resposta : ( 2 - x²) / x²