The difference of 32 · x² / (x² + 8 · x + 15) - 14 · x² / (x² - 9) is equal to [18 · x³ - 166 · x²] / [(x + 3) · (x + 5) · (x - 3)]. (Correct choice: B)
What is the result of the subtraction between two algebraic rational functions?
In this question we have a subtraction between two rational functions, which have to be simplified by algebra properties. The complete procedure is presented below:
32 · x² / (x² + 8 · x + 15) - 14 · x² / (x² - 9) Given
32 · x² / [(x + 3) · (x + 5)] - 14 · x² / [(x + 3) · (x - 3)] Factorization
[x² / (x + 3)] · [32 / (x + 5) - 14 / (x - 3)] Distributive and associative properties
[x² / (x + 3)] · [32 · (x - 3) - 14 · (x + 5)] / [(x + 5) · (x - 3)] Subtraction of rational numbers with distinct denominators
[x² / (x + 3)] · [32 · x - 96 - 14 · x - 70] / [(x + 5) · (x - 3)] Distributive property / (- 1) · a = - a
[x² / (x + 3)] · (18 · x - 166) / [(x + 5) · (x - 3)] Distributive property / Definitions of addition and subtraction
[18 · x³ - 166 · x²] / [(x + 3) · (x + 5) · (x - 3)] Mutiplication between rational numbers / Multiplication between powers / Distributive property
The difference of 32 · x² / (x² + 8 · x + 15) - 14 · x² / (x² - 9) is equal to [18 · x³ - 166 · x²] / [(x + 3) · (x + 5) · (x - 3)]. (Correct choice: B)
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