What is the name of this theorem.

[Miike012]

1. The problem statement, all variables and given/known data
What is the name of this when your try to prove this.... I want to know so I can search on google because this totally does not make any logical sence to me. This one does actually, however when I start having to manipulate I start getting lost.....

If : a/b = c/d = e/f ; Let equal to k then: k -----> a = kb ; c = kd ; e = kf

Prove : (2a^4b^2 + 3a^2e^2 - 5e^4f) / (2b^6 + 3b^2f^2 -5k^4f^5) = a^4/b^4

[D H]

Prove : (2a^4b^2 + 3a^2e^2 - 5e^4f) / (2b^6 + 3b^2f^2 -5k^4f^5) = a^4/b^4
That looks wrong. Are you sure that the k^4f^5 term in the denominator on the left-hand side is correct? Getting rid of the factor of k^4 in that term yields this:

Prove : (2a^4b^2 + 3a^2e^2 - 5e^4f) / (2b^6 + 3b^2f^2 -5f^5) = a^4/b^4

This statement is provable given that a/b=c/d=e/f≠0 and assuming that the numerator and denominator on the left hand side are not zero.