# Simplify: `(2a^2 - 12a + 18)/(3a^2 - 12)` `xx`  `(a^2 + a - 6)/(4a^2 - 36)` Keep (  ) around binomial factors.  Leave answer in factored form.

lemjay | High School Teacher | (Level 2) Senior Educator

Posted on

`(2a^2-12a+18)/(3a^2-12)xx(a^2+a-6)/(4a^2-36)`

To simplify,  factor the polynomials.

`=(2(a^2-6a+9))/(3(a^2-4))xx(a^2+a-6)/(4(a^2-9))`

`=(2(a-3)(a-3))/(3(a+2)(a-2))xx((a+3)(a-2))/(4(a-3)(a+3))`

Then, cancel the common factors between numerators and denominators.

`=(a-3)/(3(a+2))xx1/(2(a+3))`

`=(a-3)/(6(a+2))`

Hence, `(2a^2-12a+18)/(3a^2-12)xx(a^2+a-6)/(4a^2-36)=(a-3)/(6(a+2))` .
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}