How to multiply rational expressions

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PSAT Math › How to multiply rational expressions

Questions 1 - 2
1

Simplify (4x)/(x2 – 4) * (x + 2)/(x2 – 2x)

(4x2 + 8x)/(x4 + 8x)

x/(x – 2)2

4/(x – 2)2

x/(x + 2)

4/(x + 2)2

Explanation

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.

2

what is 6/8 X 20/3

5

120/11

18/160

9/40

3/20

Explanation

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

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