[tex]Solution, \frac{11}{\left(x+2\right)}=\frac{4}{\left(x-1\right)}\quad :\quad x=\frac{19}{7}\quad \left(\mathrm{Decimal:\quad }x=2.71429\dots \right)[/tex]
[tex]Steps:[/tex]
[tex]\frac{11}{\left(x+2\right)}=\frac{4}{\left(x-1\right)}[/tex]
[tex]\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c, 11\left(x-1\right)=\left(x+2\right)\cdot \:4[/tex]
[tex]\mathrm{Expand\:}11\left(x-1\right):\quad 11x-11, \mathrm{Expand\:}\left(x+2\right)\cdot \:4:\quad 4x+8, 11x-11=4x+8[/tex]
[tex]\mathrm{Add\:}11\mathrm{\:to\:both\:sides}, 11x-11+11=4x+8+11[/tex]
[tex]\mathrm{Simplify}, 11x=4x+19[/tex]
[tex]\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}, 11x-4x=4x+19-4x[/tex]
[tex]Simplify, 7x=19[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}7, \frac{7x}{7}=\frac{19}{7}[/tex]
[tex]\mathrm{Simplify}, x=\frac{19}{7}[/tex]
[tex]\mathrm{The\:Correct\:Answer\:is\:D.\:x=\frac{19}{7}}[/tex]
[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]
[tex]\mathrm{-Austint1414}[/tex]
