Question

What is the quotient

Answer 1

\[\frac{x^2-16}{2x^2-9x+4}\div \frac{2x^2+14x+24}{4x+4}=\frac{x^2-16}{2x^2-9x+4}\times \frac{4x+4}{2x^2+14x+24}\]Now let's see if we can simplify some of these terms. What would be the factors for\[x^2-16=\text{ ?}\]

Answer 2

(x+4)(x-4)?

Answer 3

Correct! Can you factor \[2x^2-9x+4= \text{ ?}\]

Answer 4

That's where I got stuck :(

Answer 5

Okay. We know it needs to be in the form of \[(2x+a)(x+b) \text{ where }ab=4 \text{ and }a+2b=-9\]So what could a and b be?

Answer 6

How would you factor -9x?

Answer 7

\[a+2b=-9\] I would guess that a=-1 and b=-4 so that \[2x^2-9x+4= (2x-1)(x-4)\] So the first term of the equation above is \[\frac{(x-4)(x+4)}{(2x-1)(x-4)}\]Can you further simplify this?

Answer 8

Yes... There is (x-4) on the numerator and (x-4) on the denominator... Cross each out and you get: