Question

Find the value of $c$, if:

$\left(\frac{3}{c+2}\right)(c+2)=(5-\frac{c}{c+2})(c+2)$.

• A. $-4$
• B. $-\frac{7}{4}$
• C. $-\frac{7}{5}$
• D. $\frac{1}{5}$

Answer 1

The correct option is B $-\frac{7}{4}$

Given, $\left(\frac{3}{c+2}\right)(c+2)=(5-\frac{c}{c+2})(c+2)$

$\Rightarrow \left(\frac{3}{c+2}\right)(c+2)=\frac{\left(5\right(c+2)-c)}{c+2}(c+2)$

$\Rightarrow 3=5c+10-c$

$\Rightarrow 3=4c+10$.

Transposing $c$ terms to one side, we get,

$\Rightarrow 4c=3-10$

$\Rightarrow 4c=-7$

$\Rightarrow c=-\frac{7}{4}$.

Hence, option $B$ is correct.