2. Subtract

(2x+3)/(2x^2-7x-15)-(x+4)/(2x^2+11x+12)

Since we are subtracting fractions, we need common

denominators. First let us factor both denominators.

 

(2x+3)/((2x+3)(x-5))-(x+4)/((2x+3)(x+4))

 

We see that both of these fractions will reduce. If we reduce

them we get

 

1/(x-5)-1/(2x+3)

 

At this point, the product of these two denominators will be the

smallest common denominator. When we cross multiply,

 

(2x+3)/((2x+3)(x-5))-(x-5)/((2x+3)(x-5))

 

we see that it really didn't do any good to simplify the first fraction,

because we had to put the factors that canceled back when we found

common denominators. However, it does do some good to reduce the

second fraction. We eliminate a factor from the denominators when

we do that.

 

Now that we have common denominators, we subtract the

numerators.

 

 

(2x+3-x+5)/((2x+3)(x-5))

and get

 

 

8/((2x+3)(x-5))

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