"Expand" means to simplify or rewrite the given equation in a more expanded form. In this equation, we are asked to expand the given expression by expanding the terms within the parentheses.
To expand an equation with negative exponents, we use the rule that states a^(-n) = 1/a^n. In this equation, we can rewrite the expressions within the parentheses as fractions with positive exponents before expanding.
The purpose of expanding an equation is to make it easier to solve or manipulate. By expanding an equation, we can see all the individual terms and simplify them in a step-by-step manner.
First, we rewrite the given equation as 3/(1-3x) + 4/(2+x)^2. Then, we expand the first term using the rule mentioned in question 2 and get 3/(1-3x) = 3(1-3x)^(-1). Similarly, we expand the second term as 4/(2+x)^2 = 4(2+x)^(-2). Finally, we can distribute the coefficients to the terms within the parentheses to get the expanded form.
No, it is not necessary to expand this equation. However, expanding it can make it easier to work with, especially if we need to simplify or solve the equation further. In some cases, expanding an equation may also provide more insights into the underlying patterns or relationships between the terms.