x+5/x^2+5x-24+x+4/x^2-x-72

Question

Its so hard!

Answer 1

For this type of problem, the goal is usually to combine the fractions into a single fraction.

 

First, factor both denominators:

 

(x+5) / (x²+5x-24) + (x+4) / (x²-x-72)

(x+5) / ((x-3)(x+8)) + (x+4) / ((x-9)(x+8))

 

Now, multiply the first fraction by (x-9)/(x-9) and the second by (x-3)/(x-3) so the fractions will have a common denominator:

 

((x-9)(x+5)) / ((x-3)(x+8)(x-9)) + ((x+4)(x-3)) / ((x-3)(x+8)(x-9))

 

Now that the denominators are the same, add the numerators just like you would a normal fraction (like 1/3 + 5/3):

 

((x-9)(x+5) + (x+4)(x-3)) / ((x-3)(x+8)(x-9))

 

Foil the numerator and combine like terms to simplify:

 

(x² + 5x - 9x - 45 + x² - 3x + 4x - 12) / ((x-3)(x+8)(x-9))

(2x² - 3x - 57) / ((x-3)(x+8)(x-9))

 

 

 

For future reference, you should put parentheses into your question to make it clear what your fractions are. I had to guess what you meant, because what you actually wrote was:

 

x + ⁵/_x² + 5x - 24 + x + ⁴/_x² - x - 72

 

which is completely different!