Reduce the following rational expression to the lowest form
1 answer:
Answer:
4x(x - 1)
Step-by-step explanation:
Factor the numerator and denominator
64 - 64x ← factor out 64x from both terms
= 64x( - 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
← cancel (x² + 1) and (x + 1) on numerator/ denominator
= ← cancel common factor 16 on numerator/ denominator
= 4x(x - 1)
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