If a,b,c are in H.P. then prove that a/(b+c), b/(c+a), c/(a+b) are in Harmonic Progressi

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Just remember this: if x,y,z are in AP, so are x+k,y+k,z+k and kx,ky, kz for any number k

a,b,c are in HP

$\Rightarrow \frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in AP,

$\Rightarrow \frac{a+b+c}{a}-1, \frac{a+b+c}{b}-1, \frac{a+b+c}{c}-1$ are in AP

$\Rightarrow \frac{b+c}{a}, \frac{a+c}{b}, \frac{a+b}{c}$ are in AP

$\Rightarrow \frac{a}{b+c}, \frac{b}{c+a}, \frac{c}{a+b}$ are in HP

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