Question

Is anyone available to help with rational expressions & equations?

Answer 1

sure

Answer 2

thank you:)

Answer 3

i worked through this problem but would like to know if i did it correctly...

2 \ (x + 1) - 5 \ (x - 2) divided by 3 \ (x - 2) + 2 \ x

Answer 4

is this it? are the brackets ive added right??\[\left(\frac2{x + 1} - \frac5{x - 2} \right)\div \left(\frac3{x - 2} + \frac2x\right)\]

Answer 5

yes, thank you

Answer 6

cool,

alright so lets simplify the first set of brackets

\[\frac2{x + 1} - \frac5{x - 2}\]

Answer 7

to add the fractions we need to get the denominators the same

Answer 8

we can use that fact that
(as long as n isn't zero) \(\large \frac nn=1\)

and the fact that multiplying anything by one dosent change its value

\[\frac{a}{b}-\frac cd=\big(\frac{a}{b}\times\frac dd\big)-\big(\frac cd\times\frac bb\big)=\frac{ad}{bd}-\frac{cb}{db}\]

Answer 9

now the denominators are the same \(bd=db\)

\[\frac{ad}{bd}-\frac{cb}{db}=\frac{ad-cb}{bd}\]

Answer 10

i think i did that correctly, for the first i got (x + 1) (x - 2) and for the second i got x (x-2)

Answer 11

as the common denominators

Answer 12

yeah that will be right.


\[\frac2{x + 1} - \frac5{x - 2}=\frac{?-?}{(x+1)(x-2)}\]

Answer 13

and
\[\frac3{x - 2} + \frac2x=\frac{...+...}{x(x-2)}\]

Answer 14

so for the first i got -3x-9 \ (x + 1) (x + 2)

Answer 15

you mean / right? instead of ( \ )

Answer 16

if so yeah thats almost right ( check the negative sign in the denominator)
\[\frac2{x + 1} - \frac5{x - 2}=\frac{2(x-2)-5(x+1)}{(x+1)(x-2)}=\frac{-3x-9}{(x+1)(x-2)}\]

Answer 17

yes, sorry just typed incorrectly...i did get (x + 1) ( x - 2) in the denominator

Answer 18

thank you...then I got (5x - 4) / x (x- 2) for the next one

Answer 19

that's absolutly right

Answer 20

so you have


\[\left(\frac2{x + 1} - \frac5{x - 2} \right)\div \left(\frac3{x - 2} + \frac2x\right)\\\,\\=\frac{-3x-9}{(x+1)(x-2)}\div \frac{5x-4}{x(x-2)}\]

Answer 21

now, dividing fractions is the same as inverting the second one and multiplying
\[\frac{-3x-9}{(x+1)(x-2)}\div \frac{5x-4}{x(x-2)}\\\,\\=\frac{-3x-9}{(x+1)(x-2)}\times\frac{x(x-2)}{5x-4}\]

Answer 22

yes thank you...then i got x (-3x - 9) / (x+1) (5x - 4)

Answer 23

that is very good,

Answer 24

now can you factor out a common factor in the numerator ?

-3x - 9 =

Answer 25

-3 (x + 3)?

Answer 26

so then it would be -3x (x + 3) in the numerator?

Answer 27

i am having trouble knowing when i have to simplify the answer further

Answer 28

ops missed an x

(-3x - 9)x / (x+1) (5x - 4)

so

-3x(x +3)/ (x+1) (5x - 4) ,


hmmm

Answer 29

it can't be simplified further

Answer 30

that is the final answer.

\[\boxed{\large\color{red}\checkmark}%unk\]

Answer 31

thanks so much...do you have time to help with another?

Answer 32

yeah i can try ,

Answer 33

thank you :) (6x^2 – 30x) / ( x^2 – x – 6) multiplied by (x^2 + 4x – 21) / (40x – 8x^2)

Answer 34

so for this one , start by factorising all the numerators and denominators, i bet things will cancel

Answer 35

i got as far as 3 (x^2 - 5x) / (x + 2) multiplied by (x + 7) / 4 (5x - x^2)

Answer 36

can you show me the step before,

with all the factors (before they have cancled)

Answer 37

6 (x^2 - 5x) / (x - 3) (x + 2) multiplied by (x + 7) (x - 3) / 8 (5x - x^2)

Answer 38

that is right,

although the first numerator and the last denominator still have a factor you can pull out of them

Answer 39

how? I didn't think (x^2 - 5x) and (5x - x^2) could be cancelled

Answer 40

(x^2 - 5x) = x(x-5)

Answer 41

and the other one (5x - x^2)=x(5-x)

Answer 42

\[\frac{a-b}{b-a}=\frac{a-b}{-(a-b)}=\frac1{-1}=-1\]

Answer 43

can you see how to cancel that bit now?

Answer 44

so (5x - x^2) becomes (x^2 - 5x) when multiplied by -1...which would make it 3 / (x + 2) multiplied by (x + 7) / -4?

Answer 45

yep !

Answer 46

now the expression is simplified
now just rearrange it a bit so it looks nicier ,

Answer 47

so 3(x + 7) / -4(x + 2)

Answer 48

YES!

Answer 49

thank you so much!

Answer 50

\[\boxed{\large\color{red}\checkmark}%unk\]

Answer 51

Great work

Answer 52

one more or did i exceed my limit :)

Answer 53

i have to eat some dinner ,

Answer 54

k...well thank you very very much!