expression 2/x-2+15/x*x -7x+10=3/x*x-x-12?

Question

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Answer 1

too many ways to interpret this. Restate using parentheses.

I'm going to guess that the equation is
2/(x - 2) + 15/(x^2 - 7x + 10) = 3/(x^2 - x - 12)
2/(x - 2) + 15/(x - 2)(x - 5) = 3/(x - 4)(x + 3)
(2(x-5) + 15)/(x - 2)(x - 5) = 3/(x - 4)(x + 3)
(2x + 5)/(x - 2)(x - 5) = 3/(x - 4)(x + 3)
(2x + 5)(x - 4)(x + 3) = 3(x - 2)(x - 5)
(2x + 5)(x^2 - x - 12) = 3x^2 -21x + 30
2x^3 - 2x^2 - 24x + 5x^2 - 5x - 60 = 3x^2 -21x + 30
2x^3 + 3x^2 - 29x - 60 = 3x^2 -21x + 30
2x^3 - 8x - 30 = 0
x^3 - 4x - 15 = 0
(x - 3)(x^2 + 3x + 5) = 0
x = (-3 ± sqrt(9 -20))/2
x = (3, (- 3 + j11)/2, (- 3 - j11)/2)

....... x^2 + 3x + 5
x - 3)x^3......... - 4x - 15
....... x^3 - 3x^2
............ + 3x^2 - 4x
............ + 3x^2 - 9x
..... ..... ..... ..... . 5x - 15
..... ..... ..... ..... . 5x - 15

Answer 2

what a big one....multiply the entire expression by x ^2 since that is the biggest denominator leaving
2x-2x^2+15-7x^3+10x^2=3-x^3-12x^2....then get all expressions on one side combining the terms
-6x^3+20x^2+2x+12=0 factor out -2
-2(3x^3-10x^2-x-6)=0