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You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
multiply the whole equation by the number in the denominator
x-2\x+4=x+1\x+10
The method is the same.
A rational algebraic expression is the ratio of two polynomials, each with rational coefficients. By suitable rescaling, both the polynomials can be made to have integer coefficients.