SAT Math : How to multiply rational expressions
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Example Questions
Example Question #1 : How To Multiply Rational Expressions
Simplify (4x)/(x2 – 4) * (x + 2)/(x2 – 2x)
(4x2 + 8x)/(x4 + 8x)
4/(x + 2)2
x/(x – 2)2
x/(x + 2)
4/(x – 2)2
4/(x – 2)2
Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.
Example Question #3 : Rational Expressions
what is 6/8 X 20/3
6/8 X 20/3 first step is to reduce 6/8 -> 3/4 (Divide top and bottom by 2)
3/4 X 20/3 (cross-cancel the threes and the 20 reduces to 5 and the 4 reduces to 1)
1/1 X 5/1 = 5
Example Question #8 : Rational Expressions
Evaluate and simplify the following product:
The procedure for multplying together two rational expressions is the same as multiplying together any two fractions: find the product of the numerators and the product of the denominators separately, and then simplify the resulting quotient as far as possible, as shown:
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