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

Question

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

Answer 1

Note: Formula To Use

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

Substituting the parameter

`\begin{gathered} Area=lw \\ \\ (2(x+3))/(x+1)=((x-3)(x+3))/(2(x+5))* w \\ \\ divide\text{ both side by }(x+3) \\ \\ (2)/(x+1)=(x-3)/(2(x+5))* w \\ \\ w=(2)/(x+1)*(2(x+5))/((x-3)) \\ \\ w=(4(x+5))/((x+1)(x-3)) \end{gathered}`

Therefore, the width is

`(4(x+5))/((x+1)(x-3))`