Mathematics: Simplify completely quantity 4 x squared minus 32 x plus 48 all over quantity 3 x squared minus 17 x minus 6.

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Simplify completely quantity 4 x squared minus 32

indiareed0orv5ul

15.03.2022

For this case we must simplify the following expression:

$\frac {4x ^ 2-32x + 48} {3x ^ 2-17x-6}$

Simplifying the numerator, dividing all the terms by 4, we have:

x ^ 2-8x + 12

We factor by looking for two numbers that when added together give -8 and when multiplied by 12. These are: -6 and -2

$-6-2 = -8\\-6 * -2 = 12$

So, we have to:

x ^ 2-8x + 12 = (x-6) (x-2)

Simplifying the denominator:

We rewrite -17x as -18x + x:

3x ^ 2-18x + x-6

We factor the highest common denominator of each group:

3x (x-6) +1 (x-6)

We factor the polynomial by factoring the highest common denominator (x-6):

(x-6) (3x + 1)

So, we have to:

3x ^ 2-17x-6 = (x-6) (3x + 1)

Substituting in the original expression we have:

$\frac {(x-6) (x-2)} {(x-6) (3x + 1)} = \frac {x-2} {3x + 1}$

$\frac {4x ^ 2-32x + 48} {3x ^ 2-17x-6} = \frac {x-2} {3x + 1}$

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