reduce the ratio

[dead eye jac]

Reduce the ratio x^2-7x+12 to lowest terms
............. .....___________
.......................x^2-16


i'ts a fraction

 

[o_O]

First step would be to factor the numerator and the denominator and to see what cancels.

 

[dead eye jac]

yeah but what do i do for the denominator because i tried to factor it by getting the square root and I end up with x-4i but we haven't done anything with imaginary numbers.

 

[jwpaine]

Reduce the ratio x^2-7x+12 to lowest terms
............. .....___________
.......................x^2-16


i'ts a fraction

\(\displaystyle \frac{x^2-7x+12}{x^2-16} = \frac{(x - 4 )(x - 3 )}{(x-4)(x+4)}\)

 

[o_O]

Difference of squares:
a[sup:2b9phyid]2[/sup:2b9phyid] - b[sup:2b9phyid]2[/sup:2b9phyid] = (a + b)(a - b)

So for that bottom expression: a[sup:2b9phyid]2[/sup:2b9phyid] = x[sup:2b9phyid]2[/sup:2b9phyid] and b[sup:2b9phyid]2[/sup:2b9phyid] = 16 (notice how the negative sign isn't included). Then, as jwpaine found, a = x and b = 4. Then, plug that into (a + b)(a - b)