Simplify (x+y/x)/(y+x/y)

Problem

(x+y/x)/(y+x/y)

Solution

1. Find common denominators for the numerator and the denominator of the complex fraction.

2. Rewrite the numerator by combining the terms over the common denominator x

(x^2+y)/x

3. Rewrite the denominator by combining the terms over the common denominator y

(y^2+x)/y

4. Express as division of two fractions by multiplying the numerator by the reciprocal of the denominator.

(x^2+y)/x⋅y/(y^2+x)

5. Multiply the numerators and denominators to find the simplified expression.

(y*(x^2+y))/(x*(y^2+x))

Final Answer

(x+y/x)/(y+x/y)=(x^2*y+y^2)/(x*y^2+x^2)

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