[(√x+1) +1]/x please show work so that I can understand^^ I'm doing a calc prerequisite packet and am stuck on this problem
-
[(√x+1) +1]/x ===> by the multiple of [(√x+1) - 1] / [(√x+1) - 1]
[(√(x+1) +1 ]/x * [(√x+1) - 1] / [(√x+1) - 1]
[ ( (√x+1) +1 ) * ((√(x+1) - 1) ] / [ x * ((√x+1) - 1) ]
[ √(x+1)√(x+1) - √(x+1) + √(x+1) - 1) ] / [ x * ((√x+1) - 1) ]
[ (x+1) - 1 ] / [ x( √(x+1) - 1 ) ]
[ x + 1 - 1 ] / [ x( √(x+1) - 1 ) ]
[ x ] / [ x( √(x+1) - 1 ) ]
[ 1 ] / [ ( √(x+1) - 1 ) ]
[(√(x+1) +1 ]/x * [(√x+1) - 1] / [(√x+1) - 1]
[ ( (√x+1) +1 ) * ((√(x+1) - 1) ] / [ x * ((√x+1) - 1) ]
[ √(x+1)√(x+1) - √(x+1) + √(x+1) - 1) ] / [ x * ((√x+1) - 1) ]
[ (x+1) - 1 ] / [ x( √(x+1) - 1 ) ]
[ x + 1 - 1 ] / [ x( √(x+1) - 1 ) ]
[ x ] / [ x( √(x+1) - 1 ) ]
[ 1 ] / [ ( √(x+1) - 1 ) ]