{"id":1090,"date":"2014-01-26T19:40:22","date_gmt":"2014-01-27T02:40:22","guid":{"rendered":"http:\/\/new-gro.dyn.hhhh.org\/joeboy\/blog\/?p=1090"},"modified":"2014-01-26T19:53:52","modified_gmt":"2014-01-27T02:53:52","slug":"mathematical-quickies-no-226","status":"publish","type":"post","link":"https:\/\/www.hhhh.org\/joeboy\/blog\/?p=1090","title":{"rendered":"Mathematical Quickies No.226"},"content":{"rendered":"<p>So for some reason I never started looking for substitutions when solving equations. It was certainly something I learned to do when analyzing circuits, but when I see a math problem I never started looking for substitutions that might simplify the problem. Until recently.<\/p>\n<p>Looking at, I think this problem, it &#8220;just clicked&#8221; &#8211; and I started looking for substitutions. Then used them to nock out answers for the next half dozen puzzle problems I tackled. Weird, since I am not doing anything I did not know before, but I just started looking at problems differently.<\/p>\n<p>This one is fairly straight forward:<\/p>\n<p>Solve: (x-a)\/b + (x-b)\/a = b\/(x-a) + a\/(x-b)<\/p>\n<p>It becomes way easier to solve after a simple substitution.<br \/>\n<a href=\"wp-content\/uploads\/2014\/01\/Mathematical_Quickies_No226.pdf\">My Solution<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>So for some reason I never started looking for substitutions when solving equations. It was certainly something I learned to do when analyzing circuits, but when I see a math problem I never started looking for substitutions that might simplify the problem. Until recently. Looking at, I think this problem, it &#8220;just clicked&#8221; &#8211; and [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,17,59],"tags":[],"class_list":["post-1090","post","type-post","status-publish","format-standard","hentry","category-math","category-puzzles","category-variable-substitutions"],"_links":{"self":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1090","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1090"}],"version-history":[{"count":6,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1090\/revisions"}],"predecessor-version":[{"id":1093,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1090\/revisions\/1093"}],"wp:attachment":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1090"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1090"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1090"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}