Question

Solve each equation. State any extraneous solutions.

$\frac{\mathbf{4}}{\mathbf{f}}\mathbf{=}\frac{\mathbf{2}}{\mathbf{f}\mathbf{-}\mathbf{3}}$

Short answer

The solution of the equation is 6.

Step-by-step solution

Step 1. State the concept for observational studies.

The linear equations in one variable is an equation which is expressed in the form of $ax+b=0$, where 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:

Step 3. Check the solution.

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

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

Since both sides are equal, the equation is correct.