Which expression is equivalent to the following complex fraction?
3\/y\u22122\/x
\u22122\/x+5\/y
\u200b<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To simplify the complex fraction (\\frac{3}{y} – \\frac{2}{x} – \\frac{2}{x} + \\frac{5}{y}), we first identify the individual fractions. The expression can be rewritten as:<\/p>\n\n\n\n [ Next, we can combine like terms. The fractions involving (y) can be combined as follows:<\/p>\n\n\n\n [ Similarly, the fractions involving (x) can also be combined:<\/p>\n\n\n\n [ Now we can combine these two results into a single expression:<\/p>\n\n\n\n [ To express this as a single fraction, we need a common denominator. The least common denominator (LCD) of (y) and (x) is (xy). We rewrite each fraction with the common denominator:<\/p>\n\n\n\n [ Now, we can combine these fractions:<\/p>\n\n\n\n [ Thus, the expression simplifies to:<\/p>\n\n\n\n [ To finalize, we can factor the numerator if needed. The numerator (8x – 4y) can be factored as:<\/p>\n\n\n\n [ Therefore, the expression can be rewritten as:<\/p>\n\n\n\n [ In conclusion, the simplified expression is (\\frac{4(2x – y)}{xy}), which maintains the relationship between the original components while consolidating the expression into a single fraction.<\/p>\n","protected":false},"excerpt":{"rendered":" Which expression is equivalent to the following complex fraction?3\/y\u22122\/x\u22122\/x+5\/y\u200b The Correct Answer and Explanation is: To simplify the complex fraction (\\frac{3}{y} – \\frac{2}{x} – \\frac{2}{x} + \\frac{5}{y}), we first identify the individual fractions. The expression can be rewritten as: [\\frac{3}{y} + \\frac{5}{y} – \\frac{2}{x} – \\frac{2}{x}] Next, we can combine like terms. The fractions involving […]<\/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-160352","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160352","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=160352"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160352\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160352"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160352"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160352"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\frac{3}{y} + \\frac{5}{y} – \\frac{2}{x} – \\frac{2}{x}
]<\/p>\n\n\n\n
\\frac{3}{y} + \\frac{5}{y} = \\frac{3 + 5}{y} = \\frac{8}{y}
]<\/p>\n\n\n\n
-\\frac{2}{x} – \\frac{2}{x} = -\\frac{2 + 2}{x} = -\\frac{4}{x}
]<\/p>\n\n\n\n
\\frac{8}{y} – \\frac{4}{x}
]<\/p>\n\n\n\n
\\frac{8}{y} = \\frac{8x}{xy} \\quad \\text{and} \\quad -\\frac{4}{x} = -\\frac{4y}{xy}
]<\/p>\n\n\n\n
\\frac{8x}{xy} – \\frac{4y}{xy} = \\frac{8x – 4y}{xy}
]<\/p>\n\n\n\n
\\frac{8x – 4y}{xy}
]<\/p>\n\n\n\n
4(2x – y)
]<\/p>\n\n\n\n
\\frac{4(2x – y)}{xy}
]<\/p>\n\n\n\n