Best way to simplify a polynomial fraction divided by a polynomial fraction as completely as possible I've been trying for the past few days to complete this question from a review booklet before I start university: Simplify as completely as possible: ( 5x^2 -9x -2 / 30x^3 + 6x^2 ) / ( x^4 -3x^2 -4 / 2x^8 +6x^7 + 4x^6 )

zaviknuogg 2022-09-16 Answered
Best way to simplify a polynomial fraction divided by a polynomial fraction as completely as possible
I've been trying for the past few days to complete this question from a review booklet before I start university:
Simplify as completely as possible:
( 5x^2 -9x -2 / 30x^3 + 6x^2 ) / ( x^4 -3x^2 -4 / 2x^8 +6x^7 + 4x^6 )
However, I've only gotten as far as this answer below:
( (x -1) / 6x^2 ) / ((x^2 +1)(x^2 -4) / (2x^4 +4x^3)(x^4 + x^3))
I can't figure out how to simplify it further. What is the best / a good way to approach such a question that consists of a polynomial fraction divided by a polynomial fraction?
Is it generally a good idea to factor each fraction first then multiply them like I attempted above, or is it better to multiply them without factoring then try to simplify one big fraction?
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Answers (2)

Rayna Aguilar
Answered 2022-09-17 Author has 9 answers
5 x 2 9 x 2 30 x 3 + 6 x 2 ÷ x 4 3 x 2 4 2 x 8 + 6 x 7 + 4 x 6 = ( x 2 ) ( 5 x + 1 ) 6 x 2 ( 5 x + 1 ) × 2 x 6 ( x + 1 ) ( x + 2 ) ( x 2 ) ( x + 2 ) ( x 2 + 1 ) = x 4 ( x + 1 ) 3 ( x 2 + 1 )
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sombereki51
Answered 2022-09-18 Author has 1 answers
simplifying we obtain
( 5 x 2 9 x 2 ) ( 2 x 8 + 6 x 7 + 4 x 6 ) ( 3 x 3 + 6 x 2 ) ( x 4 3 x 2 3 4 )
multiplying numerator and denominator out we obtain:
10 x 10 + 12 x 9 38 x 8 48 x 7 8 x 6 3 x 7 + 6 x 6 9 x 5 18 x 4 12 x 3 24 x 2
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