Question

add or subtract. simplify.
(5x)/ (x^2-x-6) - (4) / (x^2+4x+4)

Answer 1

the first thing you need to do is to factorise the denominators.

Answer 2

yes. i did that. i got 5x/ (x-3) (x+2) + 4/ (x+2) (x+2)

Answer 3

good - so now you will notice that there is a common factor in both terms in the denominators.

Answer 4

yeah x+2

Answer 5

thats right, so can now simplify this expression by pulling out that common factor as follows:\[\frac{5x}{(x-3)(x+2)}-\frac{4}{(x+2)(x+2)}=\frac{1}{x+2}(\frac{5x}{x-3}-\frac{4}{x+2})\]

Answer 6

can you now do the subtraction within the braces?

Answer 7

so why do we multiply it by 1/x+2?????

Answer 8

we pulled out the 1/(x+2) as a common factor of both terms.

Answer 9

okay.

Answer 10

e.g.:\[\frac{5x}{(x-3)(x+2)}=\frac{5x}{x-3}*\frac{1}{x+2}\]

Answer 11

okay. can you help me multiply within the brackets. i'm still not sure.

Answer 12

ok - within the braces, you first need to find the LCM (Lowest Common Multiple) of both denominators.
in this case that would be (x-3)(x+2)

Answer 13

okay. but you know how in the denominator there are 3 of (x+2).
do u still just have x+2 be ur least common multiple or do you square it. since it is used 3 times when it is factored

Answer 14

then perform the subtraction as follows:\[\frac{5x}{x-3}-\frac{4}{x+2}=\frac{5x}{x-3}*\frac{x+2}{x+2}-\frac{4}{x+2}*\frac{x-3}{x-3}=\frac{5x(x+2)-4(x-3)}{(x+2)(x-3)}\]

Answer 15

why do you think there are "3" of (x+2)?

Answer 16

because when we ffactored both sides of the denominators we got (x-3) (x+2) on one side and (x+2) (x+2) on the other side

Answer 17

but we then pulled out the common (x+2) leaving a simpler subtraction within the braces

Answer 18

okay so when u multiplied it by 1/ x+2 it got rid of one of the x+2. leaving us with only 2 instead of three

Answer 19

there is only ONE (x+2) term left within the braces:\[\frac{5x}{(x-3)(x+2)}-\frac{4}{(x+2)(x+2)}=\frac{1}{x+2}(\frac{5x}{x-3}-\frac{4}{x+2})\]
it is bit like this:\[\frac{5}{4*3}-\frac{4}{7*3}=\frac{1}{3}(\frac{5}{4}-\frac{4}{7})\]

Answer 20

or, even simpler without fractions:\[7*3 - 4*3=3(7-4)\]

Answer 21

the "common factor" 3 is pulled out of both terms leaving no 3's within the braces

Answer 22

okay.

Answer 23

right, so I worked out the subtraction within the braces above as:\[\frac{5x}{x-3}-\frac{4}{x+2}=\frac{5x}{x-3}*\frac{x+2}{x+2}-\frac{4}{x+2}*\frac{x-3}{x-3}=\frac{5x(x+2)-4(x-3)}{(x+2)(x-3)}\]

Answer 24

do you follow so far?

Answer 25

yes

Answer 26

ok - so can you simplify this resulting fraction?

Answer 27

do you cancel like terms. does it leave us with 5x-4?

Answer 28

no, you need to work this out:\[5x(x+2)-4(x-2)=\]

Answer 29

sorry that should be 4(x-3)

Answer 30

not 4(x-2)

Answer 31

as 5x^2 +10x-4x+8

Answer 32

then 5x^2+6x+8

Answer 33

^^ 4(x-3) not 4(x-2)

Answer 34

\[5x(x+2)-4(x-3)=\]

Answer 35

okay i got. it . like the way i jsut did it but instead with x-3 not x-2?

Answer 36

exactly

Answer 37

okay thank you for your help.

Answer 38

yw

Answer 39

???

Answer 40

don't forget to multiply by the common factor we took out at the beginning

Answer 41

yw == you're welcome :)

Answer 42

okay thanks.