Chapter 11.4, Problem 19PPS

To determine

To solve the below expression -

  $\frac{n^2+n-2}{n+2}\cdot \frac{4n}{n-1}$

Answer to Problem 19PPS

The answer is $4n$ .

Explanation of Solution

Given: Expression: $\frac{n^2+n-2}{n+2}\cdot \frac{4n}{n-1}$

Calculation:

Given: Expression: $\frac{n^2+n-2}{n+2}\cdot \frac{4n}{n-1}$

Simplifying the expression, we have:

  $\begin{array}{l}{n}^2+n-2=n^2+2n-n-2\\ n^2+n-2=n\left(n+2\right)-1\left(n+2\right)\\ n^2+n-2=\left(n+2\right)\left(n-1\right)\end{array}$

Solving the above expression to cancel the values with the same factors, we have:

  $\begin{array}{l}\frac{\left(n+2\right)\left(n-1\right)}{n+2}\cdot \frac{4n}{n-1}\\ =\frac{\left(n+2\right)\left(n-1\right)}{n+2}\times \frac{4n}{n-1}\\ =\frac{1}{1}\times \frac{4n}{1}\\ =4n\end{array}$

The answer is $4n$ .

Conclusion:

Hence, the answer is $4n$ .