Q51. - Algebra 2

Question

Compare the quantity in Column A and the quantity in column B. Then determine whether:

1. The quantity in Column A is greater,
2. The quantity in Column B is greater,
3. The two quantities are equal, or
4. The relationship cannot be determined from the information given.

Step-by-Step Solution

Answer

A. The quantity in Column A is greater.

Step 1. Given Information.

Given, to compare the quantities $\frac{a^2+3a-10}{a-2}$and$\frac{a^2+a-6}{a+3}$and determine which is greater.

Step 2. Explanation .

Simplifying the expression in Column A:

$\begin{array}{l}\frac{a^2+3a-10}{a-2}=\frac{\left(a+5\right)\left(a-2\right)}{\left(a-2\right)}\\ \frac{a^2+3a-10}{a-2}=a+5\end{array}$

Simplifying the expression in Column B:

$\begin{array}{l}\frac{a^2+a-6}{a+3}=\frac{\left(a-2\right)\left(a+3\right)}{\left(a+3\right)}\\ \frac{a^2+a-6}{a+3}=a-2\end{array}$

The expression   is always greater than   because adding 5 to a number is always greater than subtracting 2 from it.

Step 3. Conclusion .

Hence the quantity in column A is greater.