Chapter 1.4, Problem 63PPSE

Solution

Whether the given equations are same or no.

  $\text{Not same}$ .

Given:

The equations,

  

Concept Used:

• The opposite operation of addition is subtraction and the opposite operation of subtraction is addition.
• The opposite operation of multiplication is division and the opposite operation of division is multiplication.
• Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

Calculation:

Consider the first equation $s=\frac{n}{n+1}$ .

In order to solve the equation for n , isolate the variable n on one side by performing the basic algebraic operations as shown below

  $\begin{array}{c}s=\frac{n}{n+1}\\ s\cdot \left(n+1\right)=\frac{n}{n+1}\cdot \left(n+1\right)\\ sn+s=n\\ s=n-sn\\ s=\left(1-s\right)n\\ \frac{s}{\left(1-s\right)}=\frac{\left(1-s\right)n}{\left(1-s\right)}\\ \frac{s}{1-s}=n\end{array}$

Thus, the given equations are not same.