Chapter EP, Problem 9.6.10EP

To determine

To solve: The given mathematical expression and check your solution.

Answer to Problem 9.6.10EP

  $p=0,1$ is solution of the given mathematical expression.

Explanation of Solution

Given: $\frac{p}{p+1}+\frac{3}{p-3}+1=0$

Let $\frac{p}{p+1}+\frac{3}{p-3}+1=0$ be the given mathematical expression and it has to solve.

  $\begin{array}{l}\frac{p}{p+1}+\frac{3}{p-3}+1=0\\ \frac{p\left(p-3\right)+3\left(p+1\right)}{\left(p+1\right)\left(p-3\right)}=-1\\ \frac{p^2-3p+3p+3}{\left(p+1\right)\left(p-3\right)}=-1\\ p^2-3p+3p+3=-1\left(p+1\right)\left(p-3\right)\end{array}$

  $\begin{array}{l}{p}^2-3p+3p+3=-1\left(p^2-3p+p-3\right)\\ p^2+3=-p^2+2p+3\\ p^2+3+p^2-2p-3=0\\ 2p^2-2p=0\end{array}$

  $\begin{array}{l}2p\left(p-1\right)=0\\ 2p=0\\ p=0\\ p-1=0\\ p=1\end{array}$

Now it has to check the solution

For check solution put the answer $p=1$ in equation

  $\begin{array}{l}\frac{p}{p+1}+\frac{3}{p-3}+1=0\\ \frac{1}{1+1}+\frac{3}{1-3}+1=0\\ \frac{1}{2}+\frac{3}{-2}+1=0\\ \frac{-1+3-2}{-2}=0\\ 0=0\end{array}$

For check solution put the answer $p=0$ in equation

  $\begin{array}{l}\frac{p}{p+1}+\frac{3}{p-3}+1=0\\ \frac{0}{0+1}+\frac{3}{0-3}+1=0\\ 0+\frac{3}{-3}+1=0\\ -1+1=0\\ 0=0\end{array}$

Hence solution of the given mathematical expression is $p=0,1$ .