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# What benefits are there by simplifying algebraic fractions?

By Lisa Kelly on the 11th of June, 2012

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Once we simplify an algebraic fraction it is a lot easier to work with. For example (x^2+3x+2)/(x^2+5x+6) looks really nasty, but once it is simplified it looks like  (x+1)/(x+3) which is a lot nicer.

By Jim Gather on the 11th of June, 2012

## Simplify algebraic fractions

When simplifying algebraic expressions you must remember that fractions with numbers on the top and the bottom can be simplified by cancelling down.

Remember, whatever you do on the top, you must do on the bottom

e.g. 3/9 = 1/3

What we have done here effectively is divide by 3 on the top, and divide by 3 on the bottom.

The same can be done for fractions that have unknowns on the top and on the bottom.

e.g. 4a2/a5 = 4/a3

Remember a2 = aa, a5 = aaaaa, so a2 cancels out on the top, and on the bottom.

For the above example we must simply minus the indices.

There are several kinds of fraction that are considered to be more complex to simplify, for example:

(3x2-16x-35)/(9x2-25) = (3x + 5)(x - 7) / ( 3x + 5)(3x - 5) = (x-7)/(3x-5)

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