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Rationalizing the Denominator - with Binomial Denominators WORKSHEET
Suitable for Grades: Algebra II, IM 2
CCSS: HSA.APR.C.5, HSA.APR.D.6
CCSS Description: Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Rationalizing the Denominator - with Binomial Denominators WORKSHEET DESCRIPTION
This worksheet guides students through the process of rationalizing the denominators of fractions where the denominators are binomial.
It begins with a warm-up section designed to reinforce essential algebraic skills: expanding single and double brackets, all of which involve radicals. This foundation prepares students for Section B, where they select appropriate conjugate multipliers to rationalise denominators. The scaffolded approach ensures students understand the reasoning behind the method before advancing.
In Section C, students apply these techniques to a variety of rationalising problems with increasing complexity. The radicals and coefficients grow progressively more challenging, culminating in expressions featuring variables alongside radicals, encouraging deeper algebraic manipulation.
The worksheet steadily builds confidence and fluency in handling radicals, preparing students for more advanced algebraic concepts.
