Question

Solve each equation. State any extraneous solutions.

$\frac{3}{c}=\frac{2}{c+2}$

Short answer

The solution of the equation is $\mathbf{-}\mathbf{6}$.

Step-by-step solution

Step 1. State the concept for observational studies.

The linear equation in one variable is an equation which is expressed in the form of $ax+b=0$, where localid="1648196958283" $a$and $b$are two integers, and $x$is a variable and has only one solution.

Step 2. Solve the equation.

The equation can be solved as follows:

$\begin{array}{l}\frac{{\displaystyle 3}}{{\displaystyle c}}=\frac{{\displaystyle 2}}{{\displaystyle c+2}}\\ 3\left(c+2\right)=2c\\ 3c+6=2c\\ 3c+6-2c=2c-2c\\ c+6=0\\ c=-6\end{array}$

Step 3. Check the solution.

To check the solution, substitute$c=6$ for in the original equation,

$$\begin{gathered} \frac{3}{c}=\frac{2}{c+2} \\ \frac{3}{\left(-6\right)}=\frac{2}{\left(-6\right)+2} \\ -2=\frac{2}{-4} \\ -2=-2 \\ LHS=RHS \end{gathered}$$

Since both sides are equal, the equation is correct.