{"id":224697,"date":"2025-06-03T11:31:18","date_gmt":"2025-06-03T11:31:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224697"},"modified":"2025-06-03T11:44:16","modified_gmt":"2025-06-03T11:44:16","slug":"please-help-i-will-mark-you-as-brainliest-for-the-correct-answer-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/please-help-i-will-mark-you-as-brainliest-for-the-correct-answer-2\/","title":{"rendered":"Which expression is equivalent to the expression below"},"content":{"rendered":"\n

Which expression is equivalent to the expression below? \\frac{6c^2 + 3c}{-4c + 2} \\frac{2c + 1}{4c – 2} \\frac{3c(2c – 1)}{2c + 1} \\frac{-3c(2c + 1)^2}{4(2c – 1)^2} 3c -3c<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

We are given a complex rational expression and need to simplify it: 6c2+3c\u22124c+22c+14c\u22122\\frac{\\frac{6c^2 + 3c}{-4c + 2}}{\\frac{2c + 1}{4c – 2}}<\/p>\n\n\n\n

\n\n\n\n

Step 1: Simplify the inner expressions<\/strong><\/h3>\n\n\n\n

Numerator:<\/strong> 6c2+3c\u22124c+2\\frac{6c^2 + 3c}{-4c + 2}<\/p>\n\n\n\n

Factor the numerator and denominator:<\/p>\n\n\n\n

    \n
  • 6c2+3c=3c(2c+1)6c^2 + 3c = 3c(2c + 1)<\/li>\n\n\n\n
  • \u22124c+2=\u22122(2c\u22121)-4c + 2 = -2(2c – 1)<\/li>\n<\/ul>\n\n\n\n

    So the numerator becomes: 3c(2c+1)\u22122(2c\u22121)\\frac{3c(2c + 1)}{-2(2c – 1)}<\/p>\n\n\n\n

    \n\n\n\n

    Denominator:<\/strong> 2c+14c\u22122\\frac{2c + 1}{4c – 2}<\/p>\n\n\n\n

    Factor the denominator:<\/p>\n\n\n\n

      \n
    • 4c\u22122=2(2c\u22121)4c – 2 = 2(2c – 1)<\/li>\n<\/ul>\n\n\n\n

      So the expression becomes: 2c+12(2c\u22121)\\frac{2c + 1}{2(2c – 1)}<\/p>\n\n\n\n

      \n\n\n\n

      Step 2: Combine the complex fraction<\/strong><\/h3>\n\n\n\n

      Now write the full expression: 3c(2c+1)\u22122(2c\u22121)2c+12(2c\u22121)\\frac{\\frac{3c(2c + 1)}{-2(2c – 1)}}{\\frac{2c + 1}{2(2c – 1)}}<\/p>\n\n\n\n

      Dividing by a fraction is the same as multiplying by its reciprocal: 3c(2c+1)\u22122(2c\u22121)\u22c52(2c\u22121)2c+1\\frac{3c(2c + 1)}{-2(2c – 1)} \\cdot \\frac{2(2c – 1)}{2c + 1}<\/p>\n\n\n\n

      Cancel out common terms:<\/p>\n\n\n\n

        \n
      • 2c+12c + 1 cancels<\/li>\n\n\n\n
      • 2c\u221212c – 1 cancels<\/li>\n\n\n\n
      • 22 cancels<\/li>\n<\/ul>\n\n\n\n

        What remains is: 3c\u22c51\u22121\u22c51=\u22123c\\frac{3c \\cdot 1}{-1 \\cdot 1} = -3c<\/p>\n\n\n\n

        \n\n\n\n

        Final Answer:<\/strong><\/h3>\n\n\n\n

        \u22123c\\boxed{-3c}<\/p>\n\n\n\n

        \n\n\n\n

        Explanation<\/strong><\/h3>\n\n\n\n

        The given problem involves simplifying a complex rational expression. A complex rational expression is a fraction where the numerator or denominator (or both) is also a fraction. To simplify, we begin by factoring each part of the expression to make cancellation easier.<\/p>\n\n\n\n

        The numerator of the complex fraction is 6c2+3c\u22124c+2\\frac{6c^2 + 3c}{-4c + 2}. Factoring the numerator gives us 3c(2c+1)3c(2c + 1), and factoring the denominator gives \u22122(2c\u22121)-2(2c – 1). This transforms the numerator into 3c(2c+1)\u22122(2c\u22121)\\frac{3c(2c + 1)}{-2(2c – 1)}.<\/p>\n\n\n\n

        The denominator of the complex fraction is 2c+14c\u22122\\frac{2c + 1}{4c – 2}. Factoring the denominator results in 2(2c\u22121)2(2c – 1), giving 2c+12(2c\u22121)\\frac{2c + 1}{2(2c – 1)}.<\/p>\n\n\n\n

        Now we divide the two rational expressions. Dividing by a fraction is equivalent to multiplying by its reciprocal. So we multiply the numerator by the reciprocal of the denominator, resulting in: 3c(2c+1)\u22122(2c\u22121)\u22c52(2c\u22121)2c+1\\frac{3c(2c + 1)}{-2(2c – 1)} \\cdot \\frac{2(2c – 1)}{2c + 1}<\/p>\n\n\n\n

        We cancel out all common terms: 2c+12c + 1, 2c\u221212c – 1, and 2. We\u2019re left with: \u22123c-3c<\/p>\n\n\n\n

        This confirms the correct answer is:<\/p>\n\n\n\n

        \u22123c\\boxed{-3c}<\/strong>.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Which expression is equivalent to the expression below? \\frac{6c^2 + 3c}{-4c + 2} \\frac{2c + 1}{4c – 2} \\frac{3c(2c – 1)}{2c + 1} \\frac{-3c(2c + 1)^2}{4(2c – 1)^2} 3c -3c The Correct Answer and Explanation is: We are given a complex rational expression and need to simplify it: 6c2+3c\u22124c+22c+14c\u22122\\frac{\\frac{6c^2 + 3c}{-4c + 2}}{\\frac{2c + 1}{4c […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-224697","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224697","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=224697"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224697\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224697"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224697"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}