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Henceįactor the terms - 2 x + 4 included in the numerator as follows:Īnd use - 2 x + 4 in factored form in the rational expression to simplify We first convert (x - 2) into a rational expression. Multiply numerators and denominators (multiplication rule) but do not expand.įactor the terms included in the numerator and denominator (if possible):Īnd use the factored form in the rational expression to simplify When multiplying rationals, factor both numerators and denominators and. The division of two rational expressions is done by multiplying the first by the reciprocal of the second as follows (see divison rule above). Multiplying rational expressions is basically two simplifying problems put together. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a. Multiply numerators and denominators (multiplication rule) but do not expand as we might be able to simplifty. The division of two rational expressions is done by multiplying the first rational expression by the reciprocal of the second rational expression as follows (see divison rule above). Multiply numerators and denominators (multiplication rule)įactor the two terms in the denominator: 4 x 2 - 49 y 2 = (2x -7y)(2x + 7y) and x 2 - 1 = (x - 1)(x + 1). We divide two rational expressions by multiplying the first rational expression by the reciprocal of the second rational expression as follows:Īpply the multiplication rule (see above) Example 7.2.4 Multiply: x + 5 x 5 x 5 x2 25 Solution Factor the denominator x2 25 as a difference of squares. Next, multiply and cancel any common factors, if there are any. In this case, first factor all numerators and denominators completely. We multiply two rational expressions by multiplying their numerators and denominators as follows: Typically, rational expressions will not be given in factored form.
Multiplying rational expressions how to#
How to multiply, divide and simplify rational expressions? You need to understand each step!Īn online calculator to simplify rational expressions is included and may be used to check results. I will present the examples below with more challenging questions as you walk through the tutorial. If you have difficulties in multiplying, dividing and simplifying fractions and rational expressions, this tutorial will help you overcome those difficulties on the condition that you understand each step involved in solving these questions and also spend more time practicing if needed. How to multiply, divide and simplify rational expressions? Grade 11 examples are presented along with detailed solutions and more questions with detailed Solutions and explanations are included. How to Multiply, Divide, Simplify Rational Expressions