if :
$$\large{\frac{a}{b}=\frac{c}{d}=\frac{e}{f}}$$
prove that:
$$\large{\frac{2a^4b^2+3a^2e^2-5e^4f}{2b^6+3b^2f^2-5f^5}=\frac{a^4}{b^4}}$$

Question

if : 
$$\large{\frac{a}{b}=\frac{c}{d}=\frac{e}{f}}$$ 
prove that:
$$\large{\frac{2a^4b^2+3a^2e^2-5e^4f}{2b^6+3b^2f^2-5f^5}=\frac{a^4}{b^4}}$$

mathslover · Answer

i started like this:
$$\large{\frac{a}{b}+\frac{c}{d}+\frac{e}{f}=k}$$

mathslover · Answer

$$\large{a=bk ,\quad c=dk,\quad e=fk}$$

mathslover · Answer

i put the values of a and e there but still not getting what i wanted

anonymous · Answer

exactly with ur notations

replace $a^4$ , $a^2$ , $e^2$ and $e^4$ in numerator

anonymous · Answer

what will u get?

mathslover · Answer

yes i did : wait lemme show u what i got

mathslover · Answer

$$\large{\frac{2b^6k^4+3b^2f^2k^4-5f^5k^4}{2b^6+3b^2f^2-5f^5}}$$

mathslover · Answer

so the answer is k^4

mathslover · Answer

that is : 
$$\large{\frac{a^4}{b^4}}$$

mathslover · Answer

right?

anonymous · Answer

u got it

mathslover · Answer

oh ... i got the answer yay !!!thanks a lot @mukushla i dont know what the "hell" i was doing then? thanks again

mathslover · Answer

sorry all for disturbing u ..

anonymous · Answer

np....:)