Exercise 5.3 Class 10 Math Solutions – Multiplication & Division of Rational Expressions, Punjab Board
Solved Exercise 5.3 for Class 10 Mathematics, Punjab Board. Comprehensive step-by-step notes covering multiplication and division of rational algebraic expressions, factorization of polynomials, taking reciprocals of divisors, and canceling common factors to simplest form.
Exercise Overview
Exercise 5.3 in Unit 5: Algebraic Functions of Class 10 Punjab Board Mathematics focuses on mastering multiplication and division of algebraic rational expressions. Building on the foundational reduction and addition techniques of earlier exercises, this section challenges students to manipulate product and quotient forms of rational expressions efficiently.
The core strategy in Exercise 5.3 involves completely factorizing every numerator and denominator using techniques such as middle-term splitting, difference of two squares (a² - b² = (a-b)(a+b)), and cubic factor formulas (a³ ± b³). For division problems, students convert the operation to multiplication by taking the reciprocal (inverting) of the divisor fraction. Once expressed as a unified multiplicative product, identical linear and quadratic factors are canceled out across opposite numerators and denominators to yield the simplest rational expression.
In Punjab Board examinations (including BISE Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, Sahiwal, Sargodha, Bahawalpur, and DG Khan), questions from Exercise 5.3 frequently appear as high-scoring short questions and essential sub-parts of long questions. Practicing these structured, step-by-step solutions ensures students develop algebraic speed, avoid sign errors during division inversion, and achieve full marks in board exams.