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The area of a field can be expressed as A [tex] = \frac{2x + 6}{x + 1} [/tex]square yards. if the length is[tex]l = \frac{ {x}^{2} - 9 }{2x + 10} [/tex]what is the width? show all work.

Sagot :

Solution

Note: Formula To Use

[tex]Area=lw[/tex][tex]\begin{gathered} A=\frac{2x+6}{x+1} \\ \\ A=\frac{2(x+3)}{x+1} \\ \\ l=\frac{x^2-9}{2x+10} \\ \\ l=\frac{(x-3)(x+3)}{2(x+5)} \\ \\ w=? \end{gathered}[/tex]

Substituting the parameter

[tex]\begin{gathered} Area=lw \\ \\ \frac{2(x+3)}{x+1}=\frac{(x-3)(x+3)}{2(x+5)}\times w \\ \\ divide\text{ both side by }(x+3) \\ \\ \frac{2}{x+1}=\frac{x-3}{2(x+5)}\times w \\ \\ w=\frac{2}{x+1}\times\frac{2(x+5)}{(x-3)} \\ \\ w=\frac{4(x+5)}{(x+1)(x-3)} \end{gathered}[/tex]

Therefore, the width is

[tex]\frac{4(x+5)}{(x+1)(x-3)}[/tex]

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