Question

hey please help simplify this sum-- it's urgent!!!!

Answer 1

the required answer is 1/2bc

Answer 2

Hi ,

i ) 1/a + 1/( b + c ) = ( b + c + a )/ a( b + c )--( 1 )

ii ) 1/a - 1/( b + c ) = ( b + c - a )/a( b + c ) ---( 2 )

iii ) [ 1 + ( b² + c² - a² )/2bc ]

= [ ( 2bc + b² + c² - a² )/2bc ]

= [ ( b + c )² - a² ]/2bc

= [ ( b + c + a )( b + c - a ) ]/2bc ]

= [ ( a + b + c )(b + c - a ) ]/2bc ---( 3 )

iv ) ( a + b + c )^-2

= 1/( a + b + c )² ----- ( 4 )

Now ,

[1/a+1/b+c]/[1/a-1/b+c][1+(b²+c²-a²)/2bc](a+b+c)^-2

[ from ( 1 ), ( 2 ) , ( 3 ) and ( 4 ) ]

= [ ( 1 )/ ( 2 ) ] [ ( 3 ) ] ( 4 )

= [(a+b+c)/(b+c-a)][(a+b+c)(b+c-a)/2bc][1/(a+b+c)²]

= 1/2bc

I hope this helps you.

: )