# How do you simplify #(x^2-7x+12)/(x^2-25) div (x-4)/(x-5)#?

Dividing by a fraction = multiplying by its inverse. Also you factorise the quadratic parts and see what you can cancel

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To simplify the expression, we can start by factoring the numerator and denominator separately.

The numerator, x^2 - 7x + 12, can be factored as (x - 3)(x - 4).

The denominator, x^2 - 25, is a difference of squares and can be factored as (x - 5)(x + 5).

Next, we can rewrite the expression as [(x - 3)(x - 4)] / [(x - 5)(x + 5)] divided by (x - 4) / (x - 5).

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

Therefore, the expression simplifies to [(x - 3)(x - 4)] / [(x - 5)(x + 5)] multiplied by (x - 5) / (x - 4).

(x - 4) cancels out in the numerator and denominator, leaving us with (x - 3) / (x + 5).

Thus, the simplified expression is (x - 3) / (x + 5).

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