Chapter A5, Problem 1CP

To determine

To calculate: The simplified form of expression $\frac{x^2+8x-20}{x^2+11x+10}$.

Answer to Problem 1CP

Solution:

The simplified form of the given expression is $\frac{x-2}{x+1}$.

Explanation of Solution

Given Information:

The provided expression is $\frac{x^2+8x-20}{x^2+11x+10}$.

Formula used:

The operation with fractions:

$\frac{xy}{yz}=\frac{x}{z}$.

Take out the common factor:

$xy+yz=y\left(x+z\right)$

Calculation:

Consider the provided expression, $\frac{x^2+8x-20}{x^2+11x+10}$

Rewrite the above expression as:

$\frac{x^2+8x-20}{x^2+11x+10}=\frac{x^2+10x-2x-20}{x^2+10x+x+10}$

Use the property $xy+yz=y\left(x+z\right)$,

$\begin{array}{c}\frac{x^2+8x-20}{x^2+11x+10}=\frac{x^2+10x-2x-20}{x^2+10x+x+10}\\ =\frac{x\left(x+10\right)-2\left(x+10\right)}{x\left(x+10\right)+1\left(x+10\right)}\\ =\frac{\left(x+10\right)\left(x-2\right)}{\left(x+1\right)\left(x+10\right)}\end{array}$

Now use the property $\frac{xy}{yz}=\frac{x}{z}$ to simplify further

$\frac{x^2+8x-20}{x^2+11x+10}=\frac{\left(x-2\right)}{\left(x+1\right)}$

Therefore, the simplify form of provide equation is $\frac{\left(x-2\right)}{\left(x+1\right)}$.