{"id":18168,"date":"2026-05-02T22:27:13","date_gmt":"2026-05-02T16:27:13","guid":{"rendered":"https:\/\/mcqacademy.com\/en\/mcq\/partial-fraction-decomposition-18\/"},"modified":"2026-05-02T22:27:13","modified_gmt":"2026-05-02T16:27:13","slug":"partial-fraction-decomposition-18","status":"publish","type":"mcq","link":"https:\/\/mcqacademy.com\/en\/mcq\/partial-fraction-decomposition-18\/","title":{"rendered":"Partial Fraction Decomposition 18"},"content":{"rendered":"<p>Decompose (3*x + 30)\/((x + 6)(x + 8)) into partial fractions.<\/p>\n\n<ul class=\"quiz-options wp-block-list\">\n<li>3\/(x + 6)<\/li>\n<li>-3\/(x + 6) + 6\/(x + 8)<\/li>\n<li>6\/(x + 6) + -3\/(x + 8)<\/li>\n<li>6\/(x + 8) &#8211; -3\/(x + 6)<\/li>\n<\/ul>\n","protected":false},"author":39,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","topic":[2705],"subject":[1425],"education_level":[1896],"class_list":["post-18168","mcq","type-mcq","status-publish","hentry","topic-algebra","subject-mathematics","education_level-hsc"],"mcq_note":"Because the denominator is a product of two different linear factors, split the fraction into two simpler fractions, one over each factor. Assume A\/(x+6) + B\/(x+8). Combining gives [A(x+8)+B(x+6)]\/[(x+6)(x+8)]. Matching coefficients gives A=6, B=-3. In practice, compare the coefficient of x and the constant term on both sides to find A and B. After A and B are found, place them above their matching denominators to get the partial fraction form.","mcq_options":[{"right":"no","answer":"3\/(x + 6)"},{"right":"no","answer":"-3\/(x + 6) + 6\/(x + 8)"},{"right":"yes","answer":"6\/(x + 6) + -3\/(x + 8)"},{"right":"no","answer":"6\/(x + 8) - -3\/(x + 6)"}],"multi_answers":"no","subject_terms":[{"id":1425,"title":"Mathematics","slug":"mathematics"}],"topic_terms":[{"id":2705,"title":"Algebra","slug":"algebra"}],"_links":{"self":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq\/18168","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/mcq"}],"about":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/types\/mcq"}],"author":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/comments?post=18168"}],"wp:attachment":[{"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/media?parent=18168"}],"wp:term":[{"taxonomy":"topic","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/topic?post=18168"},{"taxonomy":"subject","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/subject?post=18168"},{"taxonomy":"education_level","embeddable":true,"href":"https:\/\/mcqacademy.com\/en\/wp-json\/wp\/v2\/education_level?post=18168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}