simplify into one fraction 9/x-1+5/x+4

Answer 1

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)].