How do you divide #(9-16x^2) / (4x-3)#?

1 Answer
Jul 21, 2015

Answer:

#(9-16x^2)/(4x-3) = -(4x+3)#
#color(white)("XXXX")##color(white)("XXXX")#(assuming #4x-3 != 0#)

Explanation:

#9-16x# is the difference of squares and therefore can be factored as:
#color(white)("XXXX")##9-16x^2 = (3-4x)(3+4x)#
#color(white)("XXXX")#or
#color(white)("XXXX")#9-16x^2 = (-1)(4x-3)(4x+3)#

So
#color(white)("XXXX")##(9-16x^2)/(4x-3)#
#color(white)("XXXX")##color(white)("XXXX")##= ((-1)cancel((4x-3))(4x+3))/(cancel(4x-3))#

#color(white)("XXXX")##color(white)("XXXX")##= -(4x+3)#