1. Jravenv

2. ybarrap

Break this up into pieces Can you factor $$m^2-4$$?

3. Jravenv

Nope I have no idea how to do any of this

4. ybarrap

$$(m+2)(m-2)=m^2-2m+2m-4=m^2-4$$ Do you see that?

5. UsukiDoll

we can factor out like terms and then cancel anything that's the same in the numerator and the denominator.

6. UsukiDoll

oh hi

7. UsukiDoll

$\frac{3m-6}{4m+12}$ let's consider this part of the problem... there is a number in common on 3m -6. What number can I factor out? also what is 3/3 and -6/3 similarly what number can I factor out? what is 4/4 and 12/4 for the denominator..

8. UsukiDoll

I can pull out a 3 for 3m-6 and I will have 3(m-2). I can pull out a 4 for 4m+12 and I will have 4(m+3)

9. UsukiDoll

$\frac{m^2+5m+6}{m^2-4}$ this requires factoring as well. We have a perfect square on the bottom of the denominator. now we just need to factor the numerator which is $m^2+5m+6$ We need to focus on all combinations that make 6 and use addition or subtraction to make a 5 the combinations of 6 are 6 and 1 1 and 6 2 and 3 3 and 2

10. UsukiDoll

6 and 1 isn't going to work . If I add them together it's 7... subtract and it's a 5. Well why can't we use this? Because our equation has double + signs... so it requires all numbers to be positive.

11. UsukiDoll

2 and 3 will work just fine. Not only is it 2 x 3 = 6, but 2+3 =5 so our $m^2+5m+6 \rightarrow (m+2)(m+3)$

12. UsukiDoll

$\frac{3(m-2)}{4(m+3)} \times \frac{(m+2)(m+3)}{(m+2)(m-2)}$

13. UsukiDoll

there are a bunch of terms to cancel out I see (m+3) on the numerator and denominator...the same case happens for (m-2) and (m+2). ANd then you are left with $\frac{3}{4}$