Chapter 6.1, Problem 20WE

To determine

To calculate: The simplified form of the expression $\frac{2w^2+w-6}{2w+4}$ and state restrictions on variable.

Answer to Problem 20WE

The simplified value of the expression $\frac{2w^2+w-6}{2w+4}$ is $\frac{n-3}{2n-5}$ and restriction is $w\ne -2$.

Explanation of Solution

Given information:

The expression $\frac{2w^2+w-6}{2w+4}$.

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 $\frac{2w^2+w-6}{2w+4}$.

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, factorize numerator by middle term splitting method and take out 2 common from denominator and then strike out common terms from the expression and simplify it as,

  $\begin{array}{c}\frac{2w^2+w-6}{2w+4}=\frac{2w^2+4w-3w-6}{2\left(w+2\right)}\\ =\frac{2w\left(w+2\right)-3\left(w+2\right)}{2\left(w+2\right)}\\ =\frac{\left(2w-3\right)\left(w+2\right)}{2\left(w+2\right)}\\ =\frac{2w-3}{2}\end{array}$

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

So, denominator will be zero when,

  $\begin{array}{c}2w+4=0\\ 2w=-4\\ w=-2\end{array}$

For denominator not to be zero, $w\ne -2$ .

Thus, the simplified value of the expression $\frac{2w^2+w-6}{2w+4}$ is $\frac{2w-3}{2}$ and restriction is $w\ne -2$.