Answer:
(i) \[5(2x+1)\,(3x+5)\,\div (2x+1)\] \[5(2x+1)\,(3x+5)\,\div (2x+1)\] \[=\frac{5(2x+1)\,(3x+5)}{2x+1}\] \[=5(3x+5)\] (ii) \[26xy(x+5)\,(y-4)\,\div \,13x(y-4)\] \[26xy(x+5)\,(y-4)\,\div \,13x(y-4)\] \[=\frac{26xy(x+5)\ (y-4)}{13x\,(y-4)}\] \[=2y(x+5)\] (iii) \[52pqr\,(p+q)\,(q+r)\,(r+p)\,\div \,104pq\] \[(q+r)\,(r+p)\] \[52pqr\,(p+q)\,(q+r)\,(r+p)\,\div \,104pq\]\[(q+r)\,(r+p)\] \[=\frac{52pqr\,(p+q)\,(q+r)\,(r+p)}{104pq(q+r)\,(r+p)}\] \[=\frac{1}{2}\,r(p+q)\] (iv) \[20(y+4)({{y}^{2}}+5y+3)\,\div \,5(y+4)\] \[20(y+4)({{y}^{2}}+5y+3)\,\div \,5(y+4)\] \[=\frac{20(x+4)\,({{y}^{2}}+5y+3)}{5(y+4)}\] \[=4({{y}^{2}}+5y+3)\] (v) \[x(x+1)\,(x+2)\,(x+3)\,\div x(x+1)\] \[x(x+1)\,(x+2)\,(x+3)\,\div x(x+1)\] \[=\frac{x(x+1)\,(x+2)\,(x+3)}{x(x+1)}\] \[=(x+2)\,(x+3)\].
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