Chapter 8, Problem 28CT

Solution

To identify:The how is it different.Simplifying rational expressions similar to simplifying fractions.

Explanation:

Compare and contrast

Simplifying rational expressions is same as simplifying fractions

You need a common denominator in addition or subtraction of rational expressions just like when dealing with rational numbers.

But in the case of simplifying rational expressions, there will be some restrictions on the variables. These restrictions will not occur in rational fractions.

For example, consider the rational expression

  $\frac{1}{x}+\frac{x-1}{x-1}$

Take the LCD to simplify the expression.

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

Thus the value of the expression is $\frac{x+1}{x}$ for $x\ne 1,0$

Thus there will be some hidden restrictions on the variable in simplifying the rational expressions.