To combine these fractions, we need a common denominator:
(9/x-1) + (5/x+4)
LCD: (x-1)(x+4)
Rewrite each fraction with the LCD as the denominator:
(9(x+4))/[(x-1)(x+4)] + (5(x-1))/[(x-1)(x+4)]
Now combine the fractions:
= [9(x+4) + 5(x-1)] / [(x-1)(x+4)]
= [9x + 36 + 5x - 5] / [(x-1)(x+4)]
= (14x + 31) /[(x-1)(x+4)]
Therefore, the sum simplifies to (14x + 31)/[(x-1)(x+4)].
simplify into one fraction 9/x-1+5/x+4
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