What is the difference?
2x+5 3x+ 5 X+ 1
x² – 3x X² – 9x x²-g

(x + 5)(x + 2) / (x³ - 9x)

Step-by-step explanation:

We need to find a common denominator.

factor each denominator

x² - 3x = x(x - 3)

x³ - 9x = x(x² - 9) = x(x + 3)(x - 3)

x² - 9 = (x + 3)(x - 3)

As the factors of the first and third denominators are subsets of the second, the second is the LCD. This immediately eliminates the last two options as possible solutions.

Now we multiply each term by the missing factor over itself (1)

(2x + 5)(x + 3) - (3x + 5) - (x + 1)(x)]

(x² - 3x)(x + 3)   (x³ - 9x)  (x² - 9)(x)

[(2x² + 11x + 15) - (3x + 5) - (x² + x)] /  (x³ - 9x)

[2x² + 11x + 15 - 3x - 5 - x² - x] /  (x³ - 9x)

(x² + 7x + 10) /  (x³ - 9x)

(x + 5)(x + 2) / (x³ - 9x)

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step-by-step explanation: