SOLUTION: 1/x = 1/y - 1/z solve for z. I think it might me something alone the lines of cross multiplying then working the equation down from there but I'm not sure..

Algebra ->  Expressions-with-variables -> SOLUTION: 1/x = 1/y - 1/z solve for z. I think it might me something alone the lines of cross multiplying then working the equation down from there but I'm not sure..      Log On


   

Question 558747: 1/x = 1/y - 1/z
solve for z.


I think it might me something alone the lines of cross multiplying then working the equation down from there but I'm not sure..
Found 2 solutions by KMST, rapaljer:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
For 1%2Fx, 1%2Fy, and 1%2Fz to exist, the three denominators have to be different from zero, and so would be their product xyz
We can eliminate denominators by ultiplying both sides of the equation times xyz
xyz%2Fx=xyz%281%2Fy+-+1%2Fz%29 --> yz=xyz%2Fy-xyz%2Fz --> yz=xz-xy
After getting rid of the denominators, we eant to get all the z's to one side of the equal sign.
yz=xz-xy --> xz-yz-xy=0 --> %28x-y%29z-xy=0 --> %28x-y%29z=xy --> z=xy%2F%28x-y%29

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx=1%2Fy-1%2Fz

Multiply both sides of the equation by the LCD which is xyz:
xyz%2A%281%2Fx%29=xyz%2A%281%2Fy%29-xyz%2A%281%2Fz%29
yz=xz-xy

In order to solve for z, you need to get all the z terms on one side. You may want to subtract xz from each side:
yz-xz+=+-xy

Factor out the z in order to get the z in one place:
z%28y-x%29=-xy

Divide both sides by (y-x):
%28z%28y-x%29%29%2F%28y-x%29+=%28-xy%29%2F%28y-x%29
z+=%28-xy%29%2F%28y-x%29


In case this is NOT the desired answer, you can multiply numerator and denominator by -1, which gives you
z+=%28xy%29%2F%28x-y%29

For additional examples and explanation like this, please see my website, and look for the page on Literal and Fractional Equations. To go to my website, use the easy-to-spell and easy-to-remember link www.mathinlivingcolor.com. At the very bottom of this page, there is a link that will take you to my Homepage.

Once you are on my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Intermediate Algebra", and look in "Chapter 2," Section 2.07 Literal and Fractional Equations for a complete, non-traditional explanation that my own students, before I retired, found a lot easier to understand than the published textbooks of that day. You should really like my MATH IN LIVING COLOR pages, where the most difficult problems are solved IN COLOR. In addition, I have a video of me teaching this topic before I retired. To find my video, look on my Homepage for the link "Rapalje Videos in Living Color."

Everything on the website is FREE. If you find something you really like, just print your own copy of it!!

If anyone needs to contact me, especially about the website, my Email address is rapaljer@seminolestate.edu. I'll be glad to help you find an explanation on my website to help you with your algebra topic!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus