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ParthKohli
Group Title
If\[x = \dfrac{4ab}{a + b}\]Then prove that\[\dfrac{x + 2a}{x  2a} + \dfrac{x + 2b}{x  2b} = 2\]
 one year ago
 one year ago
ParthKohli Group Title
If\[x = \dfrac{4ab}{a + b}\]Then prove that\[\dfrac{x + 2a}{x  2a} + \dfrac{x + 2b}{x  2b} = 2\]
 one year ago
 one year ago

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ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
@UnkleRhaukus
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
I can't believe I'm finding 9th grade so hard. :'
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Ahahahahaha well! I got it.
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Do you want to know my proof?
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
is it elegant?
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
\[x = \dfrac{4ab}{a+b} \qquad \Rightarrow \qquad \dfrac{x}{2a}=\dfrac{2ab}{a+b} ~~\text{and} ~~ \dfrac{x}{2b} = \dfrac{2a}{a+b}\]I don't know, it may be elegant.
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
i see what your doing there...
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
OK, let me continue.\[\dfrac{x + 2a}{x  2a} = \dfrac{2b + a + b}{2b  a  b}\]and\[\dfrac{x + 2b}{x2b} = \dfrac{2a + a + b}{2a  a  b}\]by componendo and dividendo property
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Oh, and in my earlier post, I meant to write\[\dfrac{x}{2a} = \dfrac{2b}{a+b}\]
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Simplifying, we get\[\dfrac{x + 2a}{x  2a} = \dfrac{3b+a}{ba}\]and\[\dfrac{x + 2b}{x2b} =\dfrac{3a+b}{a  b}\]
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
So now we can add both equations
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
\[\begin{aligned}\dfrac{x + 2a}{x  2a} + \dfrac{x+2b}{x2b} &=\dfrac{3b+a}{ba} + \dfrac{3a+b}{ab} \\ \\ \\ & = \dfrac{3ba+3a+b}{ab} \\ \\ \\ &= \dfrac{2a2b}{ab} \\ \\ \\ & = 2\end{aligned} \]
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Phew. QED
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
this is 9th grade?
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
No wait, this is 8th grade. I was just reviewing stuff.
 one year ago
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