A little lost, wondering about clearing fractions: Y = (10^6) / X - (10^6) / Z

[ddacaro]

I'm trying to create an equation for x here, can anyone point me in the right direction, my goal would be an equation for x, such as "X=.....", derrived from,

Y=(10^6)/X - (10^6)/Z

I thought I remembered how to deal with the variables in the numerators, but not in the denominators. Any help is greatly appreciated so thank you in advance ! : )

David

 

[Deleted member 4993]

I'm trying to create an equation for x here, can anyone point me in the right direction, my goal would be an equation for x, such as "X=.....", derrived from,

Y=(10^6)/X - (10^6)/Z

I thought I remembered how to deal with the variables in the numerators, but not in the denominators. Any help is greatly appreciated so thank you in advance ! : )

David

Y*10^(-6) + Z = 1/X

Now get "X"......

 

[mmm4444bot]

One way is to first isolate the ratio containing X, simplify to a proportion, cross-multiply, and then solve for X.

EG: Solve for A

B = 1/A - 1/C

Isolate the ratio containing A, by adding 1/C to each side

B + 1/C = 1/A

Add the two terms on the left, to get a proportion

(BC + 1)/C = 1/A

Cross-multiply

A(BC + 1) = C

Solve for A, by dividing each side by BC + 1

A = C/(BC + 1) :cool:

 

[ddacaro]

Ok I see , plugging in numbers, looks good, thanks very much to both of you and for your explanations, it's useful to see what you both doing so I can follow up and start plugging the holes in my algebra. Best - David

 

[JeffM]

I'm trying to create an equation for x here, can anyone point me in the right direction, my goal would be an equation for x, such as "X=.....", derrived from,

Y=(10^6)/X - (10^6)/Z

I thought I remembered how to deal with the variables in the numerators, but not in the denominators. Any help is greatly appreciated so thank you in advance ! : )

David

Another way is straightforward clearing of fractions as you initially suggested.

\(\displaystyle y = \dfrac{10^6}{x} - \dfrac{10^6}{z} \implies xyz = 10^6z + 10^6x \implies x(yz - 10^6) = 10^6z \implies\)

\(\displaystyle x = \dfrac{10^6z}{yz - 10^6}.\)

You end up in the exact same place as mmm's method.