How do you multiply and simplify \frac { 15x ^ { 2} - 960} { x ^ { 2} + 13x + 40} \cdot \frac { x ^ { 2} - 25} { x ^ { 5} - 13x ^ { 4} + 40x ^ { 3} }15x2960x2+13x+40x225x513x4+40x3?

1 Answer
Nov 22, 2016

15/x^315x3

Explanation:

Factorise:
15x^2-960=15(x^2-64)=15(x-8)(x+8)15x2960=15(x264)=15(x8)(x+8)
x^2-25=(x-5)(x+5)x225=(x5)(x+5)
x^2+13x+40=(x+8)(x+5)x2+13x+40=(x+8)(x+5)
x^5-13x^4+40x^3=x^3(x-5)(x-8)x513x4+40x3=x3(x5)(x8)
Our original expression becomes:
(15(x-8)(x+8))/((x+8)(x+5))*((x-5)(x+5))/(x^3(x-5)(x-8))15(x8)(x+8)(x+8)(x+5)(x5)(x+5)x3(x5)(x8)

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