Question

Factored form. (a^(2)+15a+56)/(a^(2)-8a+12)-(a^(2)-7a+10)/(6a^(2)-48a+72)

Answer 1

To simplify the given expression in factored form, factor the numerator and denominator separately and then plug in the factored forms into the expression. The factored form of the expression is (a + 7)(a + 8) / [(a - 2)(a - 6)] - [(a - 2)(a - 5)] / 6(a - 2)(a - 6)

Step-by-step explanation:

To simplify the given expression in factored form,

Factor the numerator and denominator separately:

Numerator: a^2 + 15a + 56 can be factored as (a + 7)(a + 8)

Denominator: a^2 - 8a + 12 can be factored as (a - 2)(a - 6)

Also, a^2 - 7a + 10 can be factored as (a - 2)(a - 5)

Finally, 6a^2 - 48a + 72 can be factored as 6(a - 2)(a - 6)

Now, plug in the factored forms of the numerator and denominator into the expression:

(a + 7)(a + 8) / [(a - 2)(a - 6)] - [(a - 2)(a - 5)] / 6(a - 2)(a - 6)