How do you divide and simplify #\frac{9x^2-4}{2x-2} -: \frac{21x^2-2x-8}{1} #?

1 Answer
Jun 5, 2018

Answer:

#(3x+2)/(2(x-1)(7x+4))#

Explanation:

#"begin by factoring numerators/denominators"#

#9x^2-4" is a "color(blue)"difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#9x^2-4=(3x-2)(3x+2)#

#2x-2=2(x-1)larr" common factor of 2"#

#21x^2-2x-8larrcolor(blue)"factor using a-c method"#

#"the factors of the product "21xx-8=-168#

#"which sum to - 2 are - 14 and + 12"#

#"split the middle term using these factors"#

#21x^2-14x+12x-8#

#=7x(3x-2)+4(3x-2)#

#=(3x-2)(7x+4)#

#"the original can now be expressed as"#

#((3x-2)(3x+2))/(2(x-1))-:((3x-2)(7x+4))/1#

#"to divide the 2 fractions change division to multiply"#
#"and turn the second fraction upside down"#
#"cancel common factors on numerator/denominator"#

#=(cancel((3x-2))(3x+2))/(2(x-1))xx1/(cancel((3x-2))(7x+4))#

#=(3x+2)/(2(x-1)(7x+4))#