For this case we must simplify the following expression:
[tex]\frac {4x ^ 2-32x + 48} {3x ^ 2-17x-6}[/tex]
Simplifying the numerator, dividing all the terms by 4, we have:
[tex]x ^ 2-8x + 12[/tex]
We factor by looking for two numbers that when added together give -8 and when multiplied by 12. These are: -6 and -2
[tex]-6-2 = -8\\-6 * -2 = 12[/tex]
So, we have to:
[tex]x ^ 2-8x + 12 = (x-6) (x-2)[/tex]
Simplifying the denominator:
We rewrite -17x as -18x + x:
[tex]3x ^ 2-18x + x-6[/tex]
We factor the highest common denominator of each group:
[tex]3x (x-6) +1 (x-6)[/tex]
We factor the polynomial by factoring the highest common denominator (x-6):
[tex](x-6) (3x + 1)[/tex]
So, we have to:
[tex]3x ^ 2-17x-6 = (x-6) (3x + 1)[/tex]
Substituting in the original expression we have:
[tex]\frac {(x-6) (x-2)} {(x-6) (3x + 1)} = \frac {x-2} {3x + 1}[/tex]
ANswer:
[tex]\frac {4x ^ 2-32x + 48} {3x ^ 2-17x-6} = \frac {x-2} {3x + 1}[/tex]
