Factor the expression completely This type of expression ari

Factor the expression completely. (This type of expression arises in calculus when using the \"Product Rule.\") 1/2x^-1/2(9x + 8)^1/2 - 9/2x^1/2(9x + 8)^-1/2

Solution

1/2 x^-1/2 ( 9x + 8)^1/2 - 9/2 x^1/2 ( 9x + 8 )^-1/2

taking out the gcf 1/2 x^1/2 (9x+8)^1/2

1/2 x^1/2 (9x+8)^1/2 [ x^-1 - 9 (9x+8)^-1 ]

1/2 x^1/2 (9x+8)^1/2 [ 1/x - 9 / (9x+8) ]

1/2 x^1/2 (9x+8)^1/2 [ (9x +8) -9x)]/x(9x +8)

1/2 x^1/2 (9x+8)^1/2[ 8/x(9x +8)]

4x^1/2(9x +8)^1/2/x(9x +8)

4/(x^1/2(9x +8)1/2)

= (4/x^1/2)*(1/(9x+8)^1/2)

=