### Home > CAAC > Chapter 10 > Lesson 10.1.2 > Problem10-21

10-21. Factor the numerator and denominator using a generic rectangle and the diamond pattern from earlier chapters.

$\frac{(x-4)(x-4)}{(x-4)(3x+2)}$

$\frac{(x-4)}{(3x+2)}$ Follow the steps in part (a). Rewrite the quotient as a product.

$\frac{(k-4)(2k+1)}{5(2k+1)}\left(\frac{10(k-3)}{(k-3)(k-4)}\right)$

Simplify the expression and then look for factors that simplify to one.

$\frac{(k-4)(2k+1)(10)(k-3)}{5(2k+1)(k-3)(k-4)}$

$\frac{(k-4)}{(k-4)}=\frac{(2k+1)}{(2k+1)}=\frac{(k-3)}{(k-3)}=1$

$\frac{10}{5}=2$
{"ft_lang_label":"__label__en","ft_lang_prob":0.7953073,"math_prob":0.9999925,"size":310,"snap":"2021-21-2021-25","text_gpt3_token_len":74,"char_repetition_ratio":0.11111111,"word_repetition_ratio":0.0,"special_character_ratio":0.2612903,"punctuation_ratio":0.11666667,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997608,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,null,null,3,null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-16T21:44:17Z\",\"WARC-Record-ID\":\"<urn:uuid:0f399b51-9d1d-4c2b-a470-f1db009e2afe>\",\"Content-Length\":\"44046\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:225ef04c-e575-4cc9-a2c7-21558f481959>\",\"WARC-Concurrent-To\":\"<urn:uuid:b02aa340-5698-4215-b90e-6801ac797d72>\",\"WARC-IP-Address\":\"104.26.7.16\",\"WARC-Target-URI\":\"https://homework.cpm.org/category/CON_FOUND/textbook/caac/chapter/10/lesson/10.1.2/problem/10-21\",\"WARC-Payload-Digest\":\"sha1:GCBZLVP36YTTFAMLAUV3VSB4MFE7DAIW\",\"WARC-Block-Digest\":\"sha1:NJFU7B6SVO4XILAC56WAGPVO6GWNSUEE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243989914.60_warc_CC-MAIN-20210516201947-20210516231947-00103.warc.gz\"}"}