2. Subtract

 

Since we are subtracting fractions, we need to find common denominators. First factor both denominators.

 

 

We see that both denominators already have a factor of x+5. The first one needs a factor of x-3, and the other one needs a factor of x-4. We multiply top and bottom of each fraction by the missing factors in their bottoms in order to build common denominators.

 

 

Multiply out the tops, because we need to subtract them, but leave the bottoms factored.

 

 

We have common denominators, so we can subtract the numerators. Remember that when we subtract, change the sign and add.

 

 

Combine

 

 

At this point we try to factor the top in order to see if the fraction will reduce, but it will not.

 

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