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Simplify (3x^2 - 15x)/(3x^2 - 13x -10)

Begin by considering the numerator and denominator separately, simplify both:

1) 3x^2 - 15x

Here, a common factor of 3x can be removed to give 3x(x^2 -5).

2) 3x^2 - 13x -10

This involves using two brackets each arranged as (ax+b)(cx+d). Unlike in 1), 3x cannot be removed as a common factor, but 3x must exist in order for 3x^2 to be present, therefore you get (3x+b)(x+d). The next thing to consider is how to multiply b and d to obtain 10, the factors of 10 are 1, 10, 2 and 5. As "-10" is in the expression to be simplified, one of the signs must be a minus. So considering 2 and 5, there are two possible answers: (3x - 2)(x+5) or (3x+2)(x-5), multiplying these out you find that the latter is the only possible solution.

Finally, putting the new simplified fraction together you get: (3x(x-5))/((3x+2)(x-5), (x-5) cancel on the numerator and denominator giving you a final, simplified, fraction of 3x/(3x+2).

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