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

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Expert Answers

terryhi | 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.

Student Comments

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**