Question 917641


The rectangle has a perimeter of {{{P=5}}} units. 
The length is {{{L=3/(x+2) }}} and the width is {{{W= 2/(x-3) }}}.

{{{P=2(L+W)}}}

What is the value of {{{x}}}?

{{{5=2(3/(x+2) +2/(x-3))}}}

{{{5=(6(x-3)/((x+2)(x-3))+4(x+2)/((x-3)(x+2)) )}}}

{{{5=(6x-18+4x+8))/((x-3)(x+2)) }}}

{{{5=(10x-10))/((x-3)(x+2)) }}}

{{{5(x-3)(x+2)=10x-10 }}}

{{{5(x^2+2x-3x-6)=10x-10 }}}

{{{5x^2+10x-15x-30-10x+10=0 }}}

{{{5x^2-15x-20=0 }}}

{{{5x^2/5-15x/5-20/5=0 }}}

{{{x^2-3x-4=0 }}}

{{{x^2+x-4x-4=0 }}}

{{{(x^2+x)-(4x+4)=0 }}}

{{{x(x+1)-4(x+1)=0 }}}

{{{(x-4)(x+1)=0 }}}

solutions:

{{{x-4=0 }}} => {{{x=4}}}

{{{x+1=0 }}}=>{{{x=-1}}}

since we have rectangle, we need only positive solution; so{{{x=4}}}