Express the rational function in partial fractions.

March 27, 2026Computer Science

$Express the rational function in partial fractions.$

ScanSolve AI Answer

March 27, 2026

Answer

\frac{A}{x+1} + \frac{B}{x+2}$$

Step 1: Express the rational function in partial fractions. We want to express $\frac{6x+1}{(x+1)(x+2)}$ in the form $\frac{A}{x+1} + \frac{B}{x+2}$ . $\frac{6x+1}{(x+1)(x+2)} = \frac{A}{x+1} + \frac{B}{x+2}$ Multiply both sides by $(x+1)(x+2)$ to clear the denominators: $6x+1 = A(x+2) + B(x+1)$

To find $A$ , set $x = -1$ :

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Express the rational function in partial fractions. We want to express (6x+1)/((x+1)(x+2)) in the form (A)/(x+1) + (B)/(x+2).

Asked on March 27, 2026Computer Science

This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.

ScanSolve AI AnswerAnswered on March 27, 2026

Step 1: Express the rational function in partial fractions. We want to express (6x+1)/((x+1)(x+2)) in the form (A)/(x+1) + (B)/(x+2). (6x+1)/((x+1)(x+2)) = (A)/(x+1) + (B)/(x+2) Multiply both sides by (x+1)(x+2) to clear the denominators: 6x+1 = A(x+2) + B(x+1) To find A, set x = -1: 6(-1)+1 = A(-1+2) + B(-1+