Chapter 6.1, Problem 15OE

To determine

To calculate: Whether the algebraic fraction can be simplified or not $\frac{4x^2-y^2}{2x-y}$.

Answer to Problem 15OE

Yes, the algebraic fraction can be simplified as $2x+y$ .

Explanation of Solution

Given information:

The expression $\frac{4x^2-y^2}{2x-y}$.

Formula used:

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

Calculation:

Consider the expression $\frac{4x^2-y^2}{2x-y}$.

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

Since, numerator can be further factorized using $X^2-Y^2=\left(X+Y\right)\left(X-Y\right)$ . So, the fraction can be simplified further as,

  $\begin{array}{c}\frac{4x^2-y^2}{2x-y}=\frac{{\left(2x\right)}^2-{\left(y\right)}^2}{\left(2x-y\right)}\\ =\frac{\left(2x-y\right)\left(2x+y\right)}{2x-y}\\ =2x+y\end{array}$

Thus, the algebraic fraction can be simplified further as $2x+y$.