What is the answer to (1 / x^2 + 2x - 8) + (5 / x^2 + 3x - 4)

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1 Answer

x^2 + 2x - 8 = (x + 4)(x - 2)

x^2 + 3x - 4 = (x + 4)(x - 1)

1 / (x^2 + 2x - 8) + 5 / (x^2 + 3x - 4)

1 / ( (x+4)(x-2) ) + 5 / ( (x+4)(x-1) )

(x-1) / ( (x+4)(x-2)(x-1) ) + 5(x-2) / ( (x+4)(x-1)(x-2) )

( (x-1) + 5(x-2) ) / ( (x+4)(x-2)(x-1) )

(x - 1 + 5x - 10) / ( (x+4)(x-2)(x-1) )

(6x - 11) / ( (x+4)(x-2)(x-1) )
by Level 13 User (103k points)

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