Question

Solve for x
1/x+2/z=2/y

Answer 1

x=(2/y-2/z)^-1

Answer 2

How does the power to negative one happen?

Answer 3

Yah, that would work, but probably not the answer you were expecting :)

Answer 4

Here's the idea:
Step 1: isolate the term with the x in it:
\[\frac{1}{x} = \frac{2}{y} - \frac{2}{z}\]

Answer 5

multiply both by x/1?

Answer 6

Yes, you could continue that way.

Answer 7

But that will create a bit of a mess.

Answer 8

ok, how should i continue?

Answer 9

Consider this, if we had
\[\frac{1}{x} = \frac{2}{3}\]
Then we could say that
\[\frac{x}{1} = \frac{3}{2}\]

Answer 10

Flip both fractions :)

Answer 11

Suppose you add the two fractions on the right hand side.

Answer 12

2/z and 2/y?

Answer 13

after flipping everything though?

Answer 14

\[\frac{2}{y} - \frac{2}{z} = \frac{2z - 2y}{yz}\]

Answer 15

You want to add first, then flip.

Answer 16

I can add two different fractions together?

Answer 17

so, 1/x + 2/z = 2/y
i should first subtract 2/z so i get 1/x = 2/y - 2/z

Answer 18

Trick only works when you have fraction = fraction. Not a sum or difference.

To add fractions with different denominators you need a common denominator. In this case just multiply the two denominators together

Answer 19

so I cross multiply the isolated fractions to get that crazy one?
and have x/1 = 2z-2y/yz

Answer 20

Good. Now you can flip!

Answer 21

Hum. in the previous, you had the left already flipped!

Answer 22

sorry it was supposed to be 1/x= 2z-2y/yz

Answer 23

Yah, ok. Good!

Answer 24

then I go x/1 = yz/2z-2y

Answer 25

You got it!

Answer 26

ok...so how do I get x alone? sorry! Im so confused

Answer 27

x/1 is just x :)

Answer 28

ok

Answer 29

If you want, you could follow your original train of thought: After you isolate the term with the x in it (step 1), you could multiply every term on both sides by x. But then you will still have to add the fractions (with more letters in them!!!). After that would would have to factor!

Answer 30

yeah, that would be harder.

Answer 31

Cheers!