The first equation's fractions have ab as their lowest common denominator, so we cross-multiply by ab to get: bx+ay=a^2b+b^2a. Similarly, we cross-multiply by a^2b^2 to get xb^2+ya^2=2a^2b^2. These are simultaneous equations involving x and y as variables and a and b as constants. We need to eliminate x or y between these equations, and we can do this by multiplying the first equation by b, giving b^2x+aby=a^2b^2+b^3a. We have b^2x (same as xb^2) in this equation and the second equation, so we can subtract to eliminate the x term. This gives us aby-a^2y=b^3a-a^2b^2. Factorising the left and right sides of this new equation we get y(a(b-a))=b^2a(b-a). We divide both sides of the equation by the common factor a(b-a) to get y=b^2. If we substitute this value of y into the first equation we get: bx+ab^2=a^2b+b^2a. The term b^2a (same as ab^2) is on both sides of the equation so it can be cancelled out leaving bx=a^2b, and we can divide both sides of the equation by the common factor b to give x=a^2. When we substitute these values of x and y in the original equations, we can clearly see the values are correct. One word of warning, though: we divided by a common factor that included (b-a). If b=a this factor would be zero and we can't divide by zero. But this is rather academic because in the original equations it doesn't matter if a=b, and x is still a^2 and y is still b^2.