Question

If $\frac{x+c}{x+1}=c+1$. Express $x$ in terms of $c$.
Given c is a constant, $c\ne 0$, $c\ne -1$ and $x\ne -1$.

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

Answer 1

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

$\frac{x+c}{x+1}=c+1$
Multiplying both sides by $x+1$,
$x+c=(c+1)(x+1)$
$x+c=cx+c+x+1$
$0=cx+1$
$x=-\frac{1}{c}$