SOLUTION: I am having trouble and are looking for your assistance. I am subtracting rational expressions and this problem has me tricked. (x-6)(x+3)/x^2-2x-15 divided by 9(x-5)/x^2-2x-15

Question 971896: I am having trouble and are looking for your assistance. I am subtracting rational expressions and this problem has me tricked.
(x-6)(x+3)/x^2-2x-15 divided by 9(x-5)/x^2-2x-15
with the denominators the same, do I still have to invert the divisor?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
What subtracting? You mention, "subtracting rational expressions", but you show partly using a word, division of rational expressions.

Operator precedence gives higher priority to division than to subtraction. Your ratio of rational expressions should be handled, or simplified, first. Yes, you would invert the second rational expression and multiply it by the first rational expression.

You might also try to factorize any rational expressions afterwards, depending on what your problem's goals are.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

I am having trouble and are looking for your assistance. I am subtracting rational expressions and this problem has me tricked.
(x-6)(x+3)/x^2-2x-15 divided by 9(x-5)/x^2-2x-15
with the denominators the same, do I still have to invert the divisor?

------ Changing division to multiplication, and inverting divisor
----- Cancelling trinomial in numerator and denominator
, or
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