Q(2) An algebraic fraction can be broken down into simpler parts known as "partial fractions. The algebraic fraction 5x-3/ (x+1)(x-2) can be broken into simpler parts as A/ 3(x+1)+ 7/ 3(x-2) Where 'A' is an integer value. What is the value of A?

To determine the value of \( A \) in the partial fraction decomposition, we begin by expressing the given algebraic fraction in terms of partial fractions:

\[
\frac{5x - 3}{(x+1)(x-2)} = \frac{A}{3(x+1)} + \frac{7}{3(x-2)}
\]

Now, we'll proceed by equating the right-hand side and the left-hand side of the equation.

### Step 1: Combine the right-hand side into a single fraction.

The common denominator for the right-hand side is \( 3(x+1)(x-2) \). So, we rewrite each term as

An algebraic fraction can be broken down into simpler parts known as 'partial fractions.' The algebraic fraction 5x-3/ (x+1)(x-2) can be broken into simpler parts as A/3(x+1) + 7/3(x-2). Where 'A' is an integer value. What is the value of A?

Learn how to decompose the algebraic fraction 5x-3/(x+1)(x-2) into partial fractions. The problem includes step-by-step instructions to determine the value of A in the decomposition. Suitable for students in Grades 9-11 studying algebra.

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Solution

Step 1: Combine the right-hand side into a single fraction.

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