Mathematics Problems Solution Explanation
The image displays two mathematics problems. For clarity, I will provide the complete solution for both of them:
#1. Find the LCD (Least Common Denominator).
The expression provided is (x - 2)(x + 1).
This is not a fraction, so typically we wouldn't be looking for an LCD, which is common when dealing with fractions. However, if we interpret the expression as a product of two binomials that might serve as denominators in separate fractions, then the LCD would indeed be the product itself, which is (x - 2)(x + 1).
#2. From the correct answer of #1, multiply every term by the LCD.
The hint given suggests that after multiplication, the pattern should look like:
x × (some expression) + (-2) × (some expression) = (-2) × (some expression)
Assuming that we are to distribute (x - 2)(x + 1) across each term of some expression, which is not provided, we would do so as follows for a generic term 'a':
a × (x - 2)(x + 1) = a(x^2 + x - 2x - 2)
= a(x^2 - x - 2)
Without additional context or an actual expression to work with, this is as far as we can solve. Each term in the original expression would be multiplied by (x - 2)(x + 1), distributed, and simplified as shown above.
