How do you simplify \frac { 6x ^ { 2} - 42x + 72} { 4x ^ { 2} - 24x + 32}?

1 Answer
Mar 26, 2017

(3(x-3))/(2(x-2))

Explanation:

First, you would factor both the polynomials:

(cancel6^3(x^2-7x+12))/(cancel4^2(x^2-6x+8))

and then find the zeros of the polynomials by the quadratic formula:

N. ->x^2-7x+12

x=(7+-sqrt(49-48))/2=(7+-1)/2

the zeros are 3 and 4, and you factor:

3(x^2-7x+12)=3(x-3)(x-4)

D.->x^2-6x+8

x=3+-sqrt(9-8)=3+-1 (applying the simple quadratic formula)

the zeros are 2 and 4, and you factor:

2(x^2-6x+8)=2(x-2)(x-4)

Finally you simplify:

(3(x^2-7x+12))/(2(x^2-6x+8))=(3(x-3)cancel((x-4)))/(2(x-2)cancel((x-4))) and get:

(3(x-3))/(2(x-2))