Class 10 Maths Chapter 5 Exercise 5.5 Solutions 2026 – Algebraic Fractions Notes PDF

Unit 5: Algebraic Fractions | Exercise 5.5 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 5.5 solutions for Algebraic Fractions have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.

Putting Every Skill to Work

The final exercise of this chapter asks a new kind of question: instead of just simplifying an expression, solve an equation that contains algebraic fractions. Exercise 5.5 draws on factorization, the LCM, and careful fraction handling all at once, making it the natural capstone to everything learned so far.

Key Concepts Covered in Exercise 5.5

Clearing the Fractions

The standard approach is to multiply every term in the equation by the LCM of all the denominators. This clears every fraction at once, turning the equation into an ordinary polynomial equation.

Solving the Resulting Equation

Once the fractions are cleared, the equation can be solved using earlier methods — simple rearrangement for a linear equation, or factorization/the quadratic formula if an x² term appears.

Checking for Extraneous Solutions

Because the original equation had a variable in the denominator, any solution that makes an original denominator zero must be rejected — even if it solves the cleared equation. This is the single most important safety check in this exercise.

Verifying the Final Answer

Substituting the solution back into the original fractional equation confirms both that it satisfies the equation and that it doesn’t fall on a restricted value.

Step-by-Step Solved Examples

Q. No. 1: Solve 3/x + 1 = 5, for x ≠ 0.

Multiply every term by the LCM, x: 3 + x = 5x

Rearrange: 3 = 5x − x = 4x

x = 3/4

Check: 3/(3/4) = 4, and 4 + 1 = 5 ✔ correct, and x ≠ 0 ✔ valid

Q. No. 2: Solve 2/(x−1) = 3/(x+1).

Cross-multiply (equivalent to clearing by the LCM (x−1)(x+1)):

2(x+1) = 3(x−1)

2x + 2 = 3x − 3

2 + 3 = 3x − 2x

x = 5

Check restrictions: x ≠ 1, x ≠ −1. Since x = 5 avoids both, the solution is valid.

Q. No. 3: Solve 1/(x−2) = 1/(x−2) + 1. Explain what happens.

Subtract 1/(x−2) from both sides: 0 = 1

This is never true, no matter what x is.

The equation has no solution — it is inconsistent for every value of x (except the already-restricted x = 2).

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 5.5 in the same numbered, step-by-step format.

MCQs, Short Questions & Long Questions from This Exercise

Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:

• MCQs: Quick questions on identifying the LCM needed to clear a given fractional equation
• Short Questions: Solving simple equations with one fractional term, like Q. No. 1 above
• Long Questions: Solving equations with fractions on both sides, including checking for extraneous solutions

Where This Matters Beyond This Exercise

Clearing fractions by multiplying through by the LCM is a technique that reappears constantly in higher mathematics, from solving rational equations in Intermediate algebra to simplifying formulas in physics and chemistry. This exercise is also a natural bridge into word problems involving rates, shared work, and mixtures, all of which are commonly modeled with fractional equations.

Common Mistakes Students Make in Exercise 5.5

• Forgetting to multiply every single term in the equation by the LCM, including any non-fraction terms
• Not checking the final solution against the original restrictions, missing an extraneous solution
• Making a sign error while cross-multiplying or expanding brackets
• Assuming every fractional equation has a solution, without checking for the “no solution” case shown in Q. No. 3

Why This Exercise Matters for the Board Exam

As the chapter’s final and most comprehensive exercise, this topic is a common source of a full long question, testing whether a student can combine several skills reliably under exam conditions. Explicitly checking and stating that a solution avoids the restricted values is often specifically required for full marks, even when the algebra itself is correct.

Quick Links – Chapter 5: Algebraic Fractions

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Download Exercise 5.5 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 5.5 notes free to download?

Yes, all notes on this page are completely free to view and download in PDF format.

Q2. Which board are these notes for?

These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).

Q3. What is an extraneous solution?

An extraneous solution is a value that satisfies the cleared (fraction-free) equation but makes one of the original denominators equal to zero. Because the original equation is undefined there, this value must be rejected even though it solved the simplified equation.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions related to this exercise’s topics, organized by question type to match the board paper pattern.

Q5. How can I download the PDF?

Click the “Download PDF” button above and the notes will open or download directly to your device.

Q6. Are these notes updated for the new 2026–27 syllabus?

Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.

Comments & Feedback

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