x2 3x x2 9x2 4x 3x2 4x 3 Select the correct choice belo

x^2 + 3x x^2 -9/x^2 + 4x + 3/x^2 + 4x + 3 Select the correct choice below and fill in any answer boxes within your choice (Simplify your answer Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed) x + 3x x - 9/x^2+4x+3 x notequalto

Solution

Given that

[ ( x² + 3x ) / ( x² + 4x + 3) ] - [ ( x² - 9 ) / ( x² + 4x + 3 ) ] = ( x² + 3x -x² + 9 ) / ( x² + 4x + 3 )

= ( 3x + 9 ) / ( x² + 4x + 3 )

= 3( x + 3 ) / ( x + 3 ) ( x+1 )

= 3 / ( x + 1 )

Therefore,

[ ( x² + 3x ) / ( x² + 4x + 3) ] - [ ( x² - 9 ) / ( x² + 4x + 3 ) ] = 3 / ( x + 1 )