Introduction: The single most important skill here is FACTORISING. Almost every problem becomes simple once you factorise all the numerators and denominators. Practice your factorising skills (difference of two squares, trinomials) until they are perfect.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Multiply): Simplify: 4y3x​×9x8y2​.

• Prompt 2 (Divide): Simplify: b5a2​÷b210a​.

• Prompt 3 (Reciprocal): What is the reciprocal of x+2x−1​?

• Prompt 4 (Factorise & Multiply): Simplify: 5x2−4​×x−210​.

• Prompt 5 (Factorise & Divide): Simplify: 3a+b​÷9(a+b)2​.

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Multiply): Simplify: x+1x2+5x+6​×x+2x+1​.

• Prompt 2 (Divide): Simplify: a2+aa2−9​÷a+1a−3​.

• Prompt 3 (Combined): Simplify: m−3m2−2m​×m−2m2−9​.

• Prompt 4 (Complex Factorising): Simplify: x2−92x2+5x−3​×2x−1x+3​.

• Prompt 5 (Combined): Simplify: p2−p−2p2−1​÷p−2p+1​.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Multi-step): Simplify: x2+xyx2−y2​×x−yx​.

• Prompt 2 (Multi-step): Simplify: a2−4b2a2−4ab+4b2​÷a+2ba−2b​.

• Prompt 3 (Explain): Explain the first step you should always take when asked to simplify an algebraic fraction problem involving multiplication or division.

• Prompt 4 (Challenge): Simplify: 3x+3x2−1​×x2−x6x​.

• Prompt 5 (Challenge): Simplify: a2−b2a2+ab−2b2​÷a+ba+2b​.

Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Three Fractions): Simplify: x2−1x2−4​×x+2x+1​÷x−1x−2​.

• Prompt 2 (Abstract): Simplify: a+b+c(a+b)2−c2​.

• Prompt 3 (Synthesis): Simplify: (x2−4x2−5x+6​)÷(x+2x−3​).

• Prompt 4 (Proof): Show that x2−xyx2−y2​÷x2x2+xy​=1.

• Prompt 5 (Challenge): Given that x2−y2=24 and x−y=2, find the value of x+yx2+2xy+y2​ without first finding x and y.