How do you simplify the expression #(b/(b+3)+2)/(b^2-2b-8)#?

1 Answer
Apr 4, 2017

Answer:

#3/(b^2-b-12)#

Explanation:

Given:#" "(b/(b+3)+2)/(b^2-2b-8 )#

#color(blue)("Consider the numerator: "b/(b+3)+2/1)#

I have deliberately chosen to write 2 as #2/1#. Although correct this is not normally done.

#color(green)([b/(b+3)]+[2/1color(red)(xx1)])#

#color(green)([b/(b+3)]+[2/1color(red)(xx(b+3)/(b+3))])#

#[b/(b+3)]+[(2b+6)/(b+3)]#

#(3b+6)/(b+3)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider the denominator: "b^2-2b-8)#

Notice that #2xx(-4)=-8 and 2-4=-2#

Write as #(b-4)(b+2)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

numerator#-:# denominator#->(3b+6)/(b+3)-:(b-4)(b+2)#

#" "=" "(3b+6)/(b+3)xx1/((b-4)(b+2))#

Factor out the 3 from #3b+6->3(b+2)#

#" "=" "(3cancel((b+2)))/(b+3)xx1/((b-4)cancel((b+2)))#

#" "=" "3/(b^2-b-12)#