Question

Simplify.. need help asap...

8/ab + 6/b

and

(3t2/(t + 2)) x ((t + 2)/t2)

thanks!!

Answer 1

The first one is \[\Large \frac{8}{ab} + \frac{6}{b}\] right?

Answer 2

yes.

Answer 3

what is the LCD in this case?

Answer 4

i don't know.

Answer 5

we have ab as the first denominator
and b as the second denominator

Answer 6

do you see how the LCD would be ab?

Answer 7

no.

Answer 8

:( I'm really bad at math. I'm sorry..

Answer 9

maybe replace a and b with numbers

Answer 10

say

a = 2
b = 3

Answer 11

okay.

Answer 12

ab = 2*3 = 6

Answer 13

i understand that.

Answer 14

if we had 1/6 + 1/3, what would the LCD be?

Answer 15

6

Answer 16

yes because we can multiply the denominator 3 by 2 to get 6

Answer 17

we can multiply top and bottom of 1/3 by 2 to get 2/6

1/6 + 1/3 turns into 1/6 + 2/6

Answer 18

from there you add straight across and leave the denominator alone

Answer 19

mhm.

Answer 20

the same idea applies here

we multiply top and bottom of the second fraction by 'a'

\[\Large \frac{8}{ab} + \frac{6}{b}\]
\[\Large \frac{8}{ab} + \frac{6{\color{red}{a}}}{b{\color{red}{a}}}\]
\[\Large \frac{8}{ab} + \frac{6a}{ab}\]

Answer 21

then you add the numerators and place that over the denominator

Answer 22

okat.

Answer 23

now I'm lost.

Answer 24

where at?

Answer 25

how do we find the answer? or did we already find it and i was lost before then? i thought I've been following.

Answer 26

do you see why I multiplied top and bottom of the second fraction by 'a'?

Answer 27

I wanted to get every denominator equal to the LCD 'ab'

Answer 28

okay

Answer 29

there's one more step to go

Answer 30

alright.

Answer 31

What does
\[\Large \frac{8}{ab} + \frac{6a}{ab}\]
simplify to?

Answer 32

8/ab + 6/ab

Answer 33

i really am lost.

Answer 34

8/ab+6/b

Answer 35

just add up the numerators

\[\Large \frac{8}{ab} + \frac{6a}{ab}=\frac{8+6a}{ab}\]

this is possible because the denominators are both equal to ab

Answer 36

okay. now how would we do the second one?

Answer 37

The second one is \[\Large \left(\frac{3t^2}{t+2}\right)\times\left(\frac{t+2}{t^2}\right)\] right?

Answer 38

t+2 on the sec on one are in a parenthesis.

Answer 39

and in the first one. its like parenthesis insides of themselves.

Answer 40

ok so this?

\[\Large \left(\frac{3t^2}{(t+2)}\right)\times\left(\frac{(t+2)}{t^2}\right)\]

Answer 41

yes that is correct.

Answer 42

first notice this cancellation

\[\Large \left(\frac{3{\color{red}{\cancel{\color{black}{t^2}}}}}{t+2}\right)\times\left(\frac{t+2}{{\color{red}{\cancel{\color{black}{t^2}}}}}\right)\]

the t^2 terms will go away leaving just

\[\Large \left(\frac{3}{(t+2)}\right)\times\left(\frac{(t+2)}{1}\right)\]

Answer 43

ok
what is the next step

Answer 44

then the (t+2) terms also cancel
\[\Large \left(\frac{3}{{\color{red}{\cancel{\color{black}{(t+2)}}}}}\right)\times\left(\frac{{\color{red}{\cancel{\color{black}{(t+2)}}}}}{1}\right)\]

Answer 45

I'm sure you see how to finish

Answer 46

so its 3?

Answer 47

yep

Answer 48

thats the easiest thing I've ever seen