factorise (a/b + b/a) + (b/c + c/b) +(c/a + a/c) + 3
Answers
Factorise:(a/b+b/a)+(b/c+c/b)+(c/a+a/c)+3. plz help
( ab + bc + ac ) ( a + b + c ) / abc
Step-by-step explanation:
( a / b + b / a ) + ( b / c + c / b ) + ( c / a + a / c ) + 3
==> ( a² + b² ) / ab + ( b² + c² )/ bc + ( c² + a² )/ac + 3
==> ( c (a² + b²) + a( b² + c² ) + b ( a² + c² ) ) / abc + 3
==> ( a²c + b²c + ab² + ac² + a²b + c²b ) / abc + 3
==> ( a²c + ac² + b²c + bc² + a²b + ab² ) / abc + 3
==> ( a²c + ac² + b²c + bc² + a²b + ab² + 3 abc ) / abc
==> ( a²c + ac² +abc + b²c + bc² +abc + a²b + ab² + abc ) / abc
==> ( ac ( a + c + b ) + bc ( b + c + a ) + ab ( a + b + c ) )/ abc
==> ( ab + bc + ac ) ( a + b + c ) / abc
Thats the factorised answer
Hope it helps ya :)
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Answer:
( ab + bc + ac ) ( a + b + c ) / abc
Step-by-step explanation:
( a / b + b / a ) + ( b / c + c / b ) + ( c / a + a / c ) + 3
==> ( a² + b² ) / ab + ( b² + c² )/ bc + ( c² + a² )/ac + 3
==> ( c (a² + b²) + a( b² + c² ) + b ( a² + c² ) ) / abc + 3
==> ( a²c + b²c + ab² + ac² + a²b + c²b ) / abc + 3
==> ( a²c + ac² + b²c + bc² + a²b + ab² ) / abc + 3
==> ( a²c + ac² + b²c + bc² + a²b + ab² + 3 abc ) / abc
==> ( a²c + ac² +abc + b²c + bc² +abc + a²b + ab² + abc ) / abc
==> ( ac ( a + c + b ) + bc ( b + c + a ) + ab ( a + b + c ) )/ abc
==> ( ab + bc + ac ) ( a + b + c ) / abc
Thats the factorised answer
Hope it helps ya :)