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How Do You Convert a Mixed Expression To a Rational Expression?

Convert 3+((x2-y2)/(x2+y2)) to a rational expression

Summary

  1. "3+((x2-y2)/(x2+y2))" is a mixed expression
  2. The '3' out in front of our entire expression is called a monomial
  3. The '((x2-y2)/(x2+y2))' is called a rational expression
  4. We multiply '3' by a fancy form of 1, which is: '((x2+y2)/(x2+y2))'
  5. With a common denominator of '(x2+y2)', we just add the numerators together
  6. Combining like terms in the numerator, we get our answer

Notes

    1. The current problem is: "3+((x2-y2)/(x2+y2))"
    2. This is a mixed expression, which is a combination of a monomial and an algebraic fraction
    1. The current problem is: "3+((x2-y2)/(x2+y2))"
    2. This is a mixed expression, which is a combination of a monomial and an algebraic fraction
    1. The current problem is: "3+((x2-y2)/(x2+y2))"
    2. This is a mixed expression, which is a combination of a monomial and an algebraic fraction
    3. The '3' out in front is one part of the expression, and is called a monomial
    1. The current problem is: "3+((x2-y2)/(x2+y2))"
    2. This is a mixed expression, which is a combination of a monomial and an algebraic fraction
    3. The '3' out in front is one part of the expression, and is called a monomial
    4. The '((x2-y2)/(x2+y2))' that follows is the other part of the expression, and is called a rational expression
    1. '((x2-y2)/(x2+y2))' is called a rational expression
    2. The entire expression is: "3+((x2-y2)/(x2+y2))"
    1. The '3' out in front of our entire expression is called a monomial
    2. Remember, multiplying a number by 1 will not change it's value
    1. The '3' out in front of our entire expression is called a monomial
    2. '(x2+y2)' is the denominator of our rational expression
    1. '(x2+y2)' is the denominator of our rational expression
    2. We're multiplying '3' by a fancy form of 1, which is: '((x2+y2)/(x2+y2))'
    3. This will turn our monomial into a rational expression with the same denominator as the rational expression in our original problem
    1. We're multiplying '3' by a fancy form of 1, which is: '((x2+y2)/(x2+y2))'
    2. This will turn our monomial into a rational expression with the same denominator as the rational expression in our original problem
    3. 3(x2+y2)/(x2+y2)
    1. '((x2-y2)/(x2+y2))' is the rational expression from our original problem
    2. (3(x2+y2)/(x2+y2))+((x2-y2)/(x2+y2))
    1. Our two fractions are: '(3(x2+y2)/(x2+y2))' and '((x2-y2)/(x2+y2))'
    2. '(x2+y2)' is the common denominator
    1. Our two numerators are: '3(x2+y2)' and '(x2-y2)'
    1. Distributing in the '3' means we need to multiply it by each term inside the parentheses
    2. 3(x2+y2) = 3x2+3y2
    3. Adding the other numerator gives us: '3x2+3y2+x2-y2'
    1. Adding the numerators gives us: '3x2+3y2+x2-y2'
    2. '(x2+y2)' is the common denominator
    3. Our expression now looks like: '(3x2+3y2+x2-y2)/(x2+y2)'
    1. Up to this point our expression looked like: '(3x2+3y2+x2-y2)/(x2+y2)'
    2. '3x2' and 'x2' are like terms
    3. '3y2' and '-y2' are like terms
    4. Now our expression now looks like: '(4x2+2y2)/(x2+y2)'
    1. Now our expression now looks like: '(4x2+2y2)/(x2+y2)'
    2. '(x2+y2)' is our denominator
    1. The mixed expression was: "3+((x2-y2)/(x2+y2))"
    2. Our rational expression is: '(4x2+2y2)/(x2+y2)'