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

Answer 1

To add the two fractions, we first need to find a common denominator:

9/(x-1) and 5/(x+4)

The common denominator would be (x-1)(x+4), so we need to rewrite each fraction with this common denominator:

9(x+4)/[(x-1)(x+4)] + 5(x-1)/[(x-1)(x+4)]

Now, we can combine the two fractions:

[9(x+4) + 5(x-1)]/[(x-1)(x+4)]

Expanding the numerators:

[9x + 36 + 5x - 5]/[(x-1)(x+4)]

Combining like terms in the numerator:

[14x + 31]/[(x-1)(x+4)]

Therefore, the sum of the two fractions simplified into one fraction is (14x + 31)/[(x-1)(x+4)].