Chapter 11.4, Problem 21MCQ

To determine

To find the expression p in

  $\frac{p}{x^2+x-12}$

Answer to Problem 21MCQ

  $p=\left(x+4\right)\left(x+5\right)$

Explanation of Solution

Given:

The expression $\frac{p}{x^2+x-12}$ simplified to $\frac{x+5}{x-3}$ .

Concept Used:

An rational expression is simplified by dividing the common factor from denominator and numerator.

Calculation:

To find the expression p in

  $\frac{p}{x^2+x-12}$

When given that $\frac{p}{x^2+x-12}$ is simplified to $\frac{x+5}{x-3}$ .

First simplify the numerator of $\frac{p}{x^2+x-12}$ and equate it to $\frac{x+5}{x-3}$ . As,

  $\begin{array}{l}\frac{p}{x^2+x-12}=\frac{x+5}{x-3}\\ \frac{p}{x^2-3x+4x-12}=\frac{x+5}{x-3}\\ \frac{p}{x\left(x-3\right)+4\left(x-3\right)}=\frac{x+5}{x-3}\\ \frac{p}{\left(x+4\right)\left(x-3\right)}=\frac{x+5}{x-3}\end{array}$

Now, above both sides to be equal p must be

  $p=\left(x+4\right)\left(x+5\right)$

This can be verified by putting $p=\left(x+4\right)\left(x+5\right)$ above as:

  $\frac{\left(x+4\right)\left(x+5\right)}{\left(x+4\right)\left(x-3\right)}=\frac{x+5}{x-3}$

Thus, the required expression p is:

  $p=\left(x+4\right)\left(x+5\right)$