Question

Reduce the following rational expression to the lowest form

Answer 1

Answer:

4x(x - 1)

Step-by-step 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)

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(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

$\frac{64x(x-1)(x+1)(x^2+1)}{16(x^2+1)(x+1)}$ ← cancel (x² + 1) and (x + 1) on numerator/ denominator

= $\frac{64x(x-1)}{16}$ ← cancel common factor 16 on numerator/ denominator

= 4x(x - 1)