How do you simplify #(x^2 + x-12 )/( 2x^2 - 3x - 9#?

1 Answer
Jun 14, 2018

Answer:

See a solution process below:

Explanation:

First, factor the numerator and denominator of the expression as:

#((x -3)(x + 4))/((2x + 3 )(x - 3))#

Next, cancel the common terms from the numerator and denominator:

#(color(red)(cancel(color(black)((x -3))))(x + 4))/((2x + 3 )color(red)(cancel(color(black)((x -3))))) =>#

#(x + 4)/(2x + 3)#

However, because we cannot divide by #0# we must ensure:

#2x + 3 != 0# and #x - 3 != 0#

Or

Condition 1:

#2x + 3 != 0#

#2x + 3 - color(red)(3) != 0 - color(red)(3)#

#2x + 0 != -3#

#2x != -3#

#(2x)/color(red)(2) != -3/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) != -3/2#

#x != -3/2#

Condition 2:

#x - 3 != 0#

#x - 3 + color(red)(3) != 0 + color(red)(3)#

#x - 0 != 3#

#x != 3#

Therefore, the simplified expression is:

#(x + 4)/(2x + 3)# Where #x != -3/2# and #x != 3#