Question

xyz/ xy+yz+xz
how do you simplify this??

Answer 1

I'm not sure what do you mean with "symplifying", I'll try to do my best:
1) \[(xyz / xy ) + yz + xz\] 2) \[z + yz + xz\] 3) \[z(y+x)\]
The last is the final result :P

Answer 2

i dont understand how you got the step 1

Answer 3

Well, step 1 is the same as you wrote.
In step 2 I divided the "xy" with "xy" which makes "1". That is step 2.
And step 3 is factorization :P

Answer 4

was this the original problem?
\[\frac{xyz}{xy+yz+xz}\]

Answer 5

the way you have it typed in the problem leads to it being interpreted in more than one way.

Answer 6

I think so @joemath314159! so I didn't understand it correctly T_T

Answer 7

yes joe math is correct

Answer 8

it looks as simplified as i'd want it. The only thing i can think of is:
\[xy = \frac{xyz}{z},yz = \frac{xyz}{x}, xz = \frac{xyz}{y}\]
so the denominator of the fraction becomes:
\[xy+yz+xz = \frac{xyz}{z}+\frac{xyz}{x}+\frac{xyz}{y} xyz(\frac{1}{z}+\frac{1}{x}+\frac{1}{y})\]
Now your whole fraction looks like:
\[\frac{xyz}{xyz(\frac{1}{z}+\frac{1}{x}+\frac{1}{y})} = \frac{1}{\frac{1}{z}+\frac{1}{x}+\frac{1}{y}}\]
While that looks a little cleaner (less variables), i dont know...having fractions in the denominator of a fraction seems taboo lol

Answer 9

oops, in my second equation line there should be an equal sign inbetween:
\[\cdots \frac{xyz}{y} = xyz\cdots \]

Answer 10

ok! that makes complete sense because the variables are supposed to appear as little as possible..thanks!!