Question

What is the simplified form of x plus 1 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x plus 3 ?

Answer 1

x² + x - 6 = x² + 3 x - 2 x - 6 = x ( x + 3 ) - 2 ( x + 3 ) = ( x + 3 ) ( x - 2 )
x² + 5 x + 4 = x² + x + 4 x + 4 = x ( x + 1 ) + 4 ( x + 1 ) = ( x + 1 ) ( x + 4 )
( x + 1 ) / ( x² + x - 6 ) : ( x² + 5 x + 4 ) / ( x + 3 ) =
= ( x + 1 ) / ( x² + x + 6 ) · ( x + 3 ) / ( x² + 5 x + 4 ) =
= ( x + 1 ) / ( x + 3 ) ( x - 2 ) · ( x + 3 ) / ( x + 1 ) ( x + 4 ) =
= 1 / ( x - 2)( x + 4 )