problem involving loop rules (circuits)

**dno21** · November 8th 2009, 05:17 PM

here we go math wiz's

i have simplified the equation to this, i am trying to solve for x and i don't kn ow what to do when there is arithmetic in the denominator ...help!

[(xyz)]/[(p)-(xy)+(xz)] = d-q+p

all i am searching for is an implicit solution obviously, but i am completely drawing a blank

**Bacterius** · November 8th 2009, 06:01 PM

What the ? Don't put brackets everywhere ! Isn't it better to understand when it's written like this ?

$\frac{\ xyz}{p - xy + xz} = d - p + q$

(click on the equation too see how it is written and update your post).

**dno21** · November 8th 2009, 06:11 PM

$<br /> \frac{\ xyz}{p - xy + xz} = d - q + p<br />$

any ideas?

and thank you bacterius, yes it is much easier

**bigwave** · November 8th 2009, 07:16 PM

$xyz = (d -q + p)(p - xy + xz)$

distribute...
$<br /> xyz = dp - dxy + dxz - qp + qxy -qxz + p^2 - pxy + pxz$

get all terms with x on right side

$xyz + dxy - dxz - qxy + qxz + pxy - pxz = dp -qp+ p^2$

factor out x

$x(yz + dy - dz - qy + qz + py - pz) = dp-qp + p^2$

divide leaving x by itself

$x = \frac{dp -qp+ p^2}{yz + dy - dz - qy + qz + py - pz}$

or

$x = \frac{p(d -q+ p)}{y(z + d - q+ p) - z(d- q + p)}$

**earboth** · November 9th 2009, 12:56 PM

Originally Posted by dno21

here we go math wiz's

i have simplified the equation to this, i am trying to solve for x and i don't kn ow what to do when there is arithmetic in the denominator ...help!

[(xyz)]/[(p)-(xy)+(xz)] = d-q+p

all i am searching for is an implicit solution obviously, but i am completely drawing a blank

1. Multiply both sides of the equation by the denominator.

2. Expand the brackets at the RHS.

3. Collect all terms containing the factor x at the LHS, all other Terms at the RHS.

4. Factor out x. Divide by the bracket.

5. You should come out with: $x = \dfrac{p \cdot (d + p - q)}{y(z + d + p - q) - z(d + p - q)}$

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