Question

Solve for $x$: $\frac{9}{x+2}-\frac{5}{x+3}=\frac{4}{x+1};x\ne \{-1,-2,-3\}$.

• A. $7$
• B. $9$
• C. $2$
• D. $5$

Answer 1

Answer: (A)

$7$

Given

$\frac{9}{x+2}-\frac{5}{x+3}=\frac{4}{x+1}$

$\Rightarrow \frac{9(x+3)-5(x+2)}{(x+3)(x+2)}=\frac{4}{x+1}$

$\Rightarrow \frac{9x+27-5x-10}{(x+3)(x+2)}=\frac{4}{x+1}$

$\Rightarrow (4x+17)(x+1)=4(x+3)(x+2)$

$\Rightarrow 4x^2+17x+4x+17=4x^2+12x+8x+24$

$\Rightarrow 21x+17=20x+24$

$\Rightarrow x=7$