Question

simplify (5/4x^2y)-(y/14xz)

Answer 1

ok, this one is more tricky. I assume this is the question?\[\frac{5}{4x^2y}-\frac{y}{14xz}\]so we have 'x', 'y' and 'z' as variables here?

Answer 2

?

Answer 3

can you please confirm whether I have the question correct?

Answer 4

yess .

Answer 5

ok, so first step is to get a common denominator - do you know how to do that?

Answer 6

yes it would be 14xz(4x^2y) for the first fraction and 4x^2y(14xz) for the second

Answer 7

yes - you can do that but have you been taught how to work out the "lowest common multiple"?

Answer 8

uhmmm yea . but im not sure that would be used here

Answer 9

working out the LCM means you get simpler equations to work with.

Answer 10

we can do it your way first and then I can show you how to use LCM method later

Answer 11

okayy then

Answer 12

so, remember that any number multiplied by one is the same number.
therefore:\[\frac{5}{4x^2y}=\frac{5}{4x^2y}\times\frac{14xz}{14xz}\]agreed?

Answer 13

where did the y go?

Answer 14

I am just looking at the first term here:\[\frac{5}{4x^2y}=\frac{5}{4x^2y}\times1=\frac{5}{4x^2y}\times\frac{14xz}{14xz}\]since:\[\frac{14xz}{14xz}=1\]

Answer 15

okayy .

Answer 16

so that then gives:\[\frac{5}{4x^2y}=\frac{5}{4x^2y}\times1=\frac{5}{4x^2y}\times\frac{14xz}{14xz}=\frac{70xz}{56x^3yz}\]ok?

Answer 17

u do have x ^ 3 right ? and z ^ 2 ?

Answer 18

not z 6 2 , scratch that

Answer 19

z ^ 2 *

Answer 20

ok, now lets look at the next term:\[\frac{y}{14xz}=\frac{y}{14xz}\times1=\frac{y}{14xz}\times\frac{4x^2y}{4x^2y}=\frac{4x^2y^2}{56x^3yz}\]agreed?

Answer 21

absolutely .

Answer 22

good, so now we can say that:\[\frac{5}{4x^2y}-\frac{y}{14xz}=\frac{70xz}{56x^3yz}-\frac{4x^2y^2}{56x^3yz}\]make sense?

Answer 23

yess . those r the equations you just got right ?

Answer 24

yes

Answer 25

okay then .

Answer 26

so now we have two fractions that have the same denominator, which means we can safely combine the numerators to get:\[\frac{5}{4x^2y}-\frac{y}{14xz}=\frac{70xz}{56x^3yz}-\frac{4x^2y^2}{56x^3yz}=\frac{70xz-4x^2y^2}{56x^3yz}\]

Answer 27

okay . now do we add/subtract common terms?

Answer 28

you can't actually add/subtract common terms here as there are none.
what you need to do next is to factorise the numerator.

Answer 29

im not sure how to do that .

Answer 30

you can see the numerator has 'x' in both terms and also that 70 and 4 are both divisible by 2

Answer 31

so then the numerator will look like ... 2x(35z-2xy^2)

Answer 32

exactly! so we get:\[\frac{5}{4x^2y}-\frac{y}{14xz}=\frac{70xz}{56x^3yz}-\frac{4x^2y^2}{56x^3yz}=\frac{70xz-4x^2y^2}{56x^3yz}=\frac{2x(35z-2xy^2)}{56x^3yz}\]

Answer 33

now you should be able to cancel some common terms between the numerator and the denominator

Answer 34

alright , let me try and work this out .

Answer 35

great! :)

Answer 36

just kidding ! im lost already /: ugh

Answer 37

just look at what cancels out between the numerator and the denominator

Answer 38

e.g. there is a 2 in the numerator and a 56 in the denominator - so you should be able to divide numerator and denominator by 2

Answer 39

then i wwill get 28x^3yz in the denom?

Answer 40

yes

Answer 41

now you should also be able to divide numerator and denominator by 'x'

Answer 42

28x^2yz?

Answer 43

that is the correct denominator - what do you get for the numerator now?

Answer 44

(35z−2xy2)

Answer 45

perfect! you've got the right answer. :)

Answer 46

yayyyyy !!!

Answer 47

if we were to find the LCM at the start, then you wouldn't need to simplify at the end as we id here as it would naturally come out simplified.
however, I suggest you first get used to simplifying these using the method above and, once you are confident with this method, then I can show you how to make use of the LCM.

Answer 48

its such an in depth question , which is what makes it so hard , but thank you for your help! and i will want to learn lcm eventually ...

Answer 49

thats good to hear. :)