How do you divide and simplify \frac{9x^2-4}{2x-2} -: \frac{21x^2-2x-8}{1} ?
1 Answer
Jun 5, 2018
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))
