stucki'm stuck in evaluation of the expression 1/xy(x+y+z)+1/yz(x+y+z)+1/zx(x+y+z)

Expert Answers
terryhi eNotes educator| Certified Educator

1/xy(x+y+z)+1/yz(x+y+z)+1/xz(x+y+z)

The least common denominator is xyz(x+y+z)

Since this is not a full equation- it does not have "=" sign-, we cannot multiply least common denominator. But, we can combine the phrase using the least common denominator.

1/xyz(x+y+z){z+x+y}

Notice if you eliminate the bracket, the value of the equation has not changed.

giorgiana1976 | Student

Since the fractions don't have a common denominator, we'll have to find LCD:

LCD = xyz(x+y+z)

We'll multiply by LCD each fraction:

xyz(x+y+z)/xy(x+y+z)+xyz(x+y+z)/yz(x+y+z)+xyz(x+y+z)/zx(x+y+z)

We'll simplify and we'll get:

z + x + y

After the evaluation of the expression, we've get the result:

1/xy(x+y+z)+1/yz(x+y+z)+1/zx(x+y+z) = x + y + z

alone- | Student

Sorry i got  mixed up on the first part.

1/x^2y+xy^2+xyz

alone- | Student

1/x^2+xy^2+xyz+1/xyz+y^2z+yz^2+1/zx^2+xyz+z^2x