Processing Math: Done
Solution 2.1:6b
From Förberedande kurs i matematik 1
The lowest common denominator for the three terms is
x−2
x+3
x+3x+3+xx+3
x−2x−2−2
x−2
x+3
x−2
x+3
=
x−2
x+3
x
x+3
+x
x−2
−2
x−2
x+3
=
x−2
x+3
x2+3x+x2−2x−2
x2+3x−2x−6
=
x−2
x+3
x2+3x+x2−2x−2x2−6x+4x+12
Now, collect together the terms in the numerator:
x−2
x+3
x2+x2−2x2
+
3x−2x−6x+4x
+12=−x+12
x−2
x+3
NOTE: By keeping the denominator factorized during the entire calculation, we can see at the end that the answer cannot be simplified any further.