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Explicit expressions for the Moore-Penrose inverses of $M=XNY$ and a two-by-two block matrix, under appropriate conditions, have been established by Castro-Gonz\\'{a}lez et al. [Linear Algebra Appl. 471 (2015) 353-368]. Based on these results, we derive a novel expression for the Moore-Penrose inverse of $A+UV^{\\ast}$ under suitable conditions, where $A\\in \\mathbb{C}^{m\\times n}$, $U\\in \\mathbb{C}^{m\\times r}$, and $V\\in \\mathbb{C}^{n\\times r}$. 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Explicit expressions for the Moore-Penrose inverses of $M=XNY$ and a two-by-two block matrix, under appropriate conditions, have been established by Castro-Gonz\\'{a}lez et al. [Linear Algebra Appl. 471 (2015) 353-368]. Based on these results, we derive a novel expression for the Moore-Penrose inverse of $A+UV^{\\ast}$ under suitable conditions, where $A\\in \\mathbb{C}^{m\\times n}$, $U\\in \\mathbb{C}^{m\\times r}$, and $V\\in \\mathbb{C}^{n\\times r}$. 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