I don't know how to solve this.

[Sarah.N]

Hi, is there anyone who can help me?

the question:
if (5zx)/(z+x)= 3 & (4yz)/(y+z)=5 & (3xy)/(x+y)=4 ,
then 1/x + 1/y + 1/z =?

i tried two ways but i couldn't find the answer. once, i changed fractions to equivalent fractions having same denominator. but it doesn't seem to help.
then I Invert the fractions , but it didn't help either.
I really don't know how to solve it.

 

[Harry_the_cat]

I would try:
\(\displaystyle \frac{z+x}{zx}=\frac{5}{3}\)
And then split up the fraction on the left to get 1/x +1/z.
Do the same to the others then add all together and see what you get.

 

[Deleted member 4993]

Hi, is there anyone who can help me?

the question:
if (5zx)/(z+x)= 3 & (4yz)/(y+z)=5 & (3xy)/(x+y)=4 ,
then 1/x + 1/y + 1/z =?

i tried two ways but i couldn't find the answer. once, i changed fractions to equivalent fractions having same denominator. but it doesn't seem to help.
then I Invert the fractions , but it didn't help either.
I really don't know how to solve it.

5zx/(z+x) = 5/[(z+x)/(zx)] = 5/(1/x + 1/z)

continue ....

 

[Sarah.N]

I would try:
\(\displaystyle \frac{z+x}{zx}=\frac{5}{3}\)
And then split up the fraction on the left to get 1/x +1/z.
Do the same to the others then add all together and see what you get.

Thanks a ton!! :‌) it helps.

5zx/(z+x) = 5/[(z+x)/(zx)] = 5/(1/x + 1/z)

continue ....

Thank you <‌3