Why is the solution to this algebraic fraction simplification given like this and how was it reached? a b − 1 2 − a − 1 2 I have a question in my text book that asks me to simplify the above expression.I reached the solution: a a b a − b However, the textbook gives the answer as: a 2 b + a b b a − b I appreciate that the value of these two expressions is the same. However, I am unsure as to how and why the answer above was reached instead of my answer.

Question

Why is the solution to this algebraic fraction simplification given like this and how was it reached?      a                  b                  −                      1            2                              −              a                  −                      1            2                              I have a question in my text book that asks me to simplify the above expression.I reached the solution:            a              a        b                            a            −              b            However, the textbook gives the answer as:                    a        2                    b            +      a      b              b                    a      −      b      I appreciate that the value of these two expressions is the same. However, I am unsure as to how and why the answer above was reached instead of my answer.

Gemma Conley · Accepted Answer

Multiply your solution by                               a                +                  b                                      a                +                  b                     and simplify.

Pader6u · Accepted Answer

Multiply your solution by                     a            +              b                            a            +              b            , you can get the textbook answer.It is because we usually like the denominator to be rational.

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