Question

Given equation is $\frac{3}{x+1}+\frac{x+1}{3}=\frac{3}{8}+\frac{8}{3}$
If $x$ is an integer, what is the value of $x$?

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

Answer: (C)

$7$

$\frac{3}{x+1}+\frac{x+1}{3}=\frac{3}{8}+\frac{8}{3}$

$\Rightarrow$ $\frac{9+(x+1{)}^2}{3(x+1)}=\frac{9+64}{24}$

$\Rightarrow$ $\frac{9+x^2+2x+1}{3x+3}=\frac{73}{24}$

$\Rightarrow$ $24(x^2+2x+10)=73(3x+3)$

$\Rightarrow$ $24x^2+48x+240=219x+219$

$\Rightarrow$ $24x^2+48x-219x+240-219=0$

$\Rightarrow$ $24x^2-171x+21=0$

$\Rightarrow$ $3(8x^2-57x+7)=0$

$\Rightarrow$ $8x^2-57x+7=0$

$\Rightarrow$ $8x^2-56x-x+7=0$

$\Rightarrow$ $8x(x-7)-1(x-7)=0$

$\Rightarrow$ $(x-7)(8x-1)=0$

$\Rightarrow$ $x=7$ and $x=\frac{1}{8}$

$\Rightarrow$ The integer is $7$