Question

Solve each equation. State any extraneous solutions.

$\frac{\mathbf{h}\mathbf{-}\mathbf{2}}{\mathbf{h}}\mathbf{=}\frac{\mathbf{h}\mathbf{-}\mathbf{2}}{\mathbf{h}\mathbf{-}\mathbf{5}}$

Short answer

The solution of the equation is 2.

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, andx is a variable and has only one solution.

Step 2. Solve the equation.

The equation can be solved as follows:

$\begin{array}{c}\frac{h-2}{h}=\frac{h-2}{h-5}\\ \left(h-2\right)\left(h-5\right)=\left(h-2\right)h\\ h\left(h-5\right)-2\left(h-5\right)=\left(h-2\right)h\\ h^2-5h-2h+10=h^2-2h\\ -7h+10=-2h\\ -7h+2h+10=-2h+2h\\ -5h+10=0\\ -5h=-10\\ h=2\end{array}$

Step 3. Check the solution.

To check the solution, substitute $h=2$for in the original equation,

$\begin{array}{c}\frac{h-2}{h}=\frac{h-2}{h-5}\\ \frac{2-2}{2}=\frac{2-2}{2-5}\\ \frac{0}{2}=\frac{0}{-3}\\ 0=0\\ LHS=RHS\end{array}$

Since both sides are equal, the equation is correct.