Could someone pls show me why:

(m/(n+m))*(V+mK) - mK

is equivalent to:

(m/(n+m))*(V-nK)

Thx for the help

Ben

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- August 8th 2007, 11:36 AMNYKarlStumped
Could someone pls show me why:

(m/(n+m))*(V+mK) - mK

is equivalent to:

(m/(n+m))*(V-nK)

Thx for the help

Ben - August 8th 2007, 12:40 PMticbol
Let's play algebra.

{(m/(n+m))*(V+mK) - mK} =? {(m/(n+m))*(V-nK)}

Notice that [m / (m+n)] is common to both expressions. So we eliminate that to simplify the two expressions. Divide both sides by [m / (m+n)],

(V +mK) -(mK / [m /(m+n)]) =? V -nK

Then simplify. Expand the Lefthand Side,

(V +mK) -(mK * [(m+n) / m]) =? V -nK

(V +mK) -[(mK)(m+n) / m] =? V -nK

Clear the fraction, multiply both sides by m,

m(V +mK) -mK(m+n) =? mV -mnK

mV +(m^2)K -(m^2)K -mnK =? mV -mnK

mV -mnK =? mV -mnK

Yes.

So, it is shown. - August 8th 2007, 02:01 PMCaptainBlack