Fractional homogeneous expression refers to the algebraic expression with the same numerator and denominator in fractional equation, and the fractional expression cannot be further reduced after simplification. For example, x 2+y 2/x 2-2xy+y 2 is a fractional homogeneous formula, in which the numerator and denominator are quadratic polynomials and cannot be reduced in order.

Fractional homogeneous expression has important application value in advanced mathematics and engineering mathematics. It can be used to solve problems in calculus, linear algebra, differential equations and partial differential equations. The solution of fractional homogeneous formula needs to master the skills of fractional simplification, denominator rationalization and factorization, which is helpful to improve the mathematical level and solve practical problems.

It should be noted that the fractional homogeneous form is only a special algebraic form. As long as the numerator and denominator have the same degree and cannot be further reduced, it can be called fractional homogeneous form. However, the fractional homogeneous formula is not the solution to all mathematical problems, and some problems may need to be solved by other methods, so it is necessary to master a variety of problem-solving methods and choose the appropriate method according to the specific situation.