I need solve

[IlgarSky]

Hello,

I need solve this equation:

if:
y=[tex]\frac{x}{z+x}[/tex]

x=?

[Math Tutor]

y(z + x) = x
yz + yx = x
yx - x = - yz
(y - 1)x = - yz
-(1 - y)x = - yz
(1 - y)x = yz

[tex]x = \frac{yz}{1 - y}[/tex]

[IlgarSky]

Thank You very much!

[leesajohnson]

y= x/z+x

move z+x to the other side and multiple with y
y(z + x) = x

now solve it and muliple y by z+x we will get
yz + yx = x

move yz to other side and solve it
yx - x = - yz
(y - 1)x = - yz
-(1 - y)x = - yz
(1 - y)x = yz

Answer is x= yz/1-y

[Guest]

The last post is a very poor description of what is actually required to solve for X...... it is more or less a copy of what was done before several montha ago.

What is required to solve for X......

The orig. equation...... Y = X / Z + X ....This is an equation that is balanced so what you do on one side you must do on the other side to keep the balance.

What we have on the RHS is a fraction X on the top and (Z + X) on the bottom.

If we multiply the RHS by (Z + X) the (Z + X) on the bottom will cancel with it and leave X only on RHS, but we must also multiply the LHS by (Z + X) to keep balance.

So that gives ..... Y(Z + X) = X(Z + X)/(Z + X)

Result after cancelling..... Y(Z + X) = X

Now multiply out the bracket on the LHS......

This gives .....YZ + YX = X

Now we need all the terms involving X to one side....the RHS.

You take away the YX from the LHS by subtracting it from the LHS, and to keep balance you must subtract YX from the RHS.

This gives ....... YZ + YX - YX = X - YX

The +YX and -YX cancel and leave .... YZ = X - YX

We now have all terms involving X on the RHS and we can take out a common factor.....

This gives .....YZ = X(1 - Y) ......Now we have a bracket (1 - Y) multiplied by X on the RHS.

If I divide the RHS by (1 - Y) the brackets will cancel on the RHS, and to keep balance we need to divide the LHS by (1 - Y).

That gives ...... YZ/(1 - Y) = X(1 - Y)/(1 - Y)

and after cancelling gives ..... YZ/(1 - Y) = X

The brackets are not really needed, only to keep the 1 - Y together

So the answer is .... X = YZ / (1 - Y).