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Reduce the following rational expression to the lowest form


(64x^(5) - 64x)/(( 8x^(2) +8) (2x +2) )

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User Stefania
by
7.5k points

1 Answer

6 votes

Answer:

4x(x - 1)

Explanation:

Factor the numerator and denominator

64
x^(5) - 64x ← factor out 64x from both terms

= 64x(
x^(4) - 1) ← difference of squares

= 64x(x² - 1)(x² + 1) ← x² - 1 is also a difference of squares

= 64x(x - 1)(x + 1)(x² + 1)

---------------------------------

(8x² + 8)(2x + 2) ← factor out 8 and 2 from each factor

= 8(x² + 1) × 2(x + 1)

= 16(x² + 1)(x + 1)

Then expression can be written as


(64x(x-1)(x+1)(x^2+1))/(16(x^2+1)(x+1)) ← cancel (x² + 1) and (x + 1) on numerator/ denominator

=
(64x(x-1))/(16) ← cancel common factor 16 on numerator/ denominator

= 4x(x - 1)

User Tdebeus
by
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