Question

Can someone help me solve? Don't want the answer told to me, want to know how to actually solve it. t^2-t-12/t+1 (t+1/t+3)

Answer 1

So the problem is

\[\Large \frac{t^2-t-12}{t+1} \times \frac{t+1}{t+3}\]

right?

Answer 2

Yes

Answer 3

Were you able to factor t^2-t-12 ?

Answer 4

no.. i have trouble with that

Answer 5

t^2-t-12 is the same as t^2-1t-12

to factor t^2-1t-12 you need to find two numbers that

a) multiply to -12 (the last number)

AND

b) add to -1 (the middle coefficient)

Answer 6

are you able to find those two numbers?

Answer 7

12, -1?

Answer 8

12 times -1 = -12, so far so good

but...

12 plus -1 = 11

we want the two numbers to add up to -1, not 11

Answer 9

ok, so are we keeping -1 or finding a new set?

Answer 10

what's another way to multiply to -12?

Answer 11

(-6,2) (-2,6) (-12,1) (-1,12) am i even on the right track??

Answer 12

you're getting closer, but you haven't found the right pair yet

Answer 13

there's another way to multiply to -12

Answer 14

(-3,4) (-4,3)

Answer 15

which pair adds to -1 ?

Answer 16

-4,3

Answer 17

That means
\[\Large t^2-t-12\]
factors to
\[\Large (t-4)(t+3)\]
You can check by expanding out (t-4)(t+3) and you'll get the original expression back.

Answer 18

So
\[\Large \frac{t^2-t-12}{t+1} \times \frac{t+1}{t+3}\]
turns into
\[\Large \frac{(t-4)(t+3)}{t+1} \times \frac{t+1}{t+3}\]
Do you see what to do from here?

Answer 19

so is it t^3+13/t^2+4 ?

Answer 20

oops, t^3-11/t^2+4?