simplify (5/4x^2y)-(y/14xz)
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?
?
can you please confirm whether I have the question correct?
yess .
ok, so first step is to get a common denominator - do you know how to do that?
yes it would be 14xz(4x^2y) for the first fraction and 4x^2y(14xz) for the second
yes - you can do that but have you been taught how to work out the "lowest common multiple"?
uhmmm yea . but im not sure that would be used here
working out the LCM means you get simpler equations to work with.
we can do it your way first and then I can show you how to use LCM method later
okayy then
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?
where did the y go?
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:\[\frac{14xz}{14xz}=1\]
okayy .
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?
u do have x ^ 3 right ? and z ^ 2 ?
not z 6 2 , scratch that
z ^ 2 *
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?
absolutely .
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?
yess . those r the equations you just got right ?
yes
okay then .
so now we have two fractions that have the same denominator, which means we can safely combine the numerators to get:\[\frac{5}{4x^2y}-\frac{y}{14xz}=\frac{70xz}{56x^3yz}-\frac{4x^2y^2}{56x^3yz}=\frac{70xz-4x^2y^2}{56x^3yz}\]
okay . now do we add/subtract common terms?
you can't actually add/subtract common terms here as there are none. what you need to do next is to factorise the numerator.
im not sure how to do that .
you can see the numerator has 'x' in both terms and also that 70 and 4 are both divisible by 2
so then the numerator will look like ... 2x(35z-2xy^2)
exactly! so we get:\[\frac{5}{4x^2y}-\frac{y}{14xz}=\frac{70xz}{56x^3yz}-\frac{4x^2y^2}{56x^3yz}=\frac{70xz-4x^2y^2}{56x^3yz}=\frac{2x(35z-2xy^2)}{56x^3yz}\]
now you should be able to cancel some common terms between the numerator and the denominator
alright , let me try and work this out .
great! :)
just kidding ! im lost already /: ugh
just look at what cancels out between the numerator and the denominator
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
then i wwill get 28x^3yz in the denom?
yes
now you should also be able to divide numerator and denominator by 'x'
28x^2yz?
that is the correct denominator - what do you get for the numerator now?
(35z−2xy2)
perfect! you've got the right answer. :)
yayyyyy !!!
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.
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 ...
thats good to hear. :)
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