Chapter 6.1, Problem 8OE

To determine

To calculate: The simplified form of the expression $\frac{2c-2d}{2c+2d}$ and state restrictions on variable.

Answer to Problem 8OE

The simplified value of the expression $\frac{2c-2d}{2c+2d}$ is $\frac{c-d}{c+d}$ and restriction is $c\ne -d$.

Explanation of Solution

Given information:

The expression $\frac{2c-2d}{2c+2d}$.

Formula used:

The simplest form of an algebraic fraction is when numerator and denominator have no common factor other than 1 and $-1$ . Simplification is done by factorizing numerator and denominator.

Calculation:

Consider the expression $\frac{2c-2d}{2c+2d}$.

Recall that the simplest form of an algebraic fraction is when numerator and denominator have no common factor other than 1 and $-1$ . Simplification is done by factorizing numerator and denominator.

So, take out 2 common from both the numerator and the denominator and then strike out common terms and simplify it as,

  $\begin{array}{c}\frac{2c-2d}{2c+2d}=\frac{2\left(c-d\right)}{2\left(c+d\right)}\\ =\frac{c-d}{c+d}\end{array}$

To restrict the variable, exclude the value that makes the denominator zero.

So, denominator will be zero when,

  $\begin{array}{c}2c+2d=0\\ 2c=-2d\\ c=-d\end{array}$

For denominator not to be zero, $c\ne -d$.

Thus, the simplified value of the expression $\frac{2c-2d}{2c+2d}$ is $\frac{c-d}{c+d}$ and restriction is $c\ne -d$.