question_answer 12)

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

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)  \[x(x+1)\,(x+2)\,(x+3)\,\div x(x+1)\]                 \[x(x+1)\,(x+2)\,(x+3)\,\div x(x+1)\]                 \[=\frac{x(x+1)\,(x+2)\,(x+3)}{x(x+1)}\]                 \[=(x+2)\,(x+3)\].