The fractional and rational equation is the equation at which there is a fraction which numerator and a denominator are presented by rational expressions. To solve the equation - means to find all such ""x"" at which substitution the right numerical equality turns out. How to solve the fractional and rational equation? Let's consider the general algorithm of the solution of the fractional and rational equations.
Instruction
1. Transfer everything to the left member of equation. In the right member of equation there has to be zero.
2. Reduce everything in the left part to a common denominator. That is, turn expression in the left part into one fraction.
3. Further the condition of equality of fraction to zero comes into force: the fraction is considered equal to zero if the numerator is equal to zero, but the denominator is not equal. On the basis of it make a system: the numerator is equal to zero, the denominator is not equal to zero.
4. Solve the equation with numerator. Find such x values at which the numerator of fraction addresses in zero. For this purpose it is useful to factorize numerator. All expression is equal to zero in only case when one of multipliers is equal to zero at least.
5. Further it is necessary to eliminate excess x values. Perhaps two options. You can substitute the found x values in a denominator and look whether he addresses in zero at these x values. If does not address, so it ""x"" approaches and if addresses, then this x value can be rejected.
6. And it is possible to make and solve the equation: to equate a denominator to zero. Then to compare x values at which the numerator equals to zero, and at which the denominator equals to zero. If the x value is present both there, and there, then it should be rejected. In reply those x values at which the numerator is equal to zero will go, but the denominator is not equal.
7. Make check. Substitute the received x values in the equation and make sure that they really satisfy to the equation.
8. Write down the answer.