Question

Which factor can you cancel from the numerator and denominator to simplify 8-2x/3x-12? [Hint: (a−x) = − (x − a)]

Answer 1

can you notice a common factor in the numerator between the terms 8 and 2x?

Answer 2

2

Answer 3

good, so can you write the numerator with the 2 taken out as a factor?

Answer 4

sorry that kinda confused me

Answer 5

ok - you correctly found that 2 is a common factor between 8 and 2x, this means we can factor the numerator as follows:\[8-2x=2(4-x)\]agreed?

Answer 6

oh yes. i agree

Answer 7

good - now try the same thing with the denominator - what is common between 3x and 12?

Answer 8

3 so 2(x-4)

Answer 9

*3

Answer 10

perfect!
so now you end up with:\[\frac{8-2x}{3x-12}=\frac{2(4-x)}{3(x-4)}\]next, try and make use the hint given to you in the question.

Answer 11

so i cold cancel out the 4's?

Answer 12

no, what you need to do is notice that:\[(4-x)=-(x-4)\]

Answer 13

do you understand that?

Answer 14

not really

Answer 15

ok, let me try to explain...

Answer 16

ok

Answer 17

\[-(x-4)=-x-(-4)=-x+4=4-x\]does it make sense now?

Answer 18

yes

Answer 19

ok, so if we use this fact, then we can substitute:\[(4-x)=-(x-4)\]into out fraction to get:\[\frac{8-2x}{3x-12}=\frac{2(4-x)}{3(x-4)}=\frac{-2(x-4)}{3(x-4)}\]

Answer 20

make sense?

Answer 21

yes

Answer 22

ok now you should be able to see that we can cancel out \((x-4)\) from numerator and denominator.

Answer 23

makes sense now! thanks so much! tremendous help!

Answer 24

yw :)