Question

If $\frac{x+c}{x+1}=c+1$, then $x=$_____.

• A. $\frac{-1}{c}$
• B. $c-2$
• C. $\frac{c-1}{c}$
• D. $\frac{c-1}{c+1}$

Answer 1

The correct option is A $\frac{-1}{c}$

Given, $\frac{x+c}{x+1}=c+1$

$\Rightarrow x+c=(c+1)(x+1)$ …[Cross-multiplying the denominators]

$\Rightarrow x+c=cx+c+x+1$ ...[By Distribution Law]

$\Rightarrow cx+1=0$ ...[Cancelling common terms on both sides]

$\Rightarrow cx=-1$

$\Rightarrow x=\frac{-1}{c}$.

Hence, option $A$ is correct.