Express as a single fraction: `(x-1)/(2x^2 -x-3)-(x+2)/(2x^2 +x-6)` Thanks ` ` 

Expert Answers
lemjay eNotes educator| Certified Educator


To express this as single fraction, factor the denominators.

`=(x-1)/((x+1)(2x-3)) -(x+2)/((x+2)(2x-3))`

Notice that in the second fraction x+2 is present both on the numerator and denominator. So, cancel its common factor to simplify.


Then, multiply all the different factors in the denominators to get the LCD. 


Hence, the LCD of the two fractions is (x+1)(2x-3).

Since the denominator of the first fraction contains all the factors of the LCD, then it is only the equivalent fraction of 1/(2x-3) must be determined.

To get its equivalent fraction, notice its denominator have only one of the factor of the LCD which is (2x-3). So to have a denominator od (x+1)(2x-3), multiply its numerator and denominator by the missing factor (x+1).



Now that they have same denominators, subtract them.

`= ((x-1)-(x+1))/((x+1)(2x-3))`




Hence,   `(x-1)/(2x^2-x-3)-(x+2)/(2x^2+x-6)=-2/((x+1)(2x-3))`  .