3/27/2021 0 Comments Solve 5 1 X 10
Rational expressions typically contain a variable in the denominator.This is not always the case; sometimes we will be left with a quadratic equation.
To solve it, rewrite it in standard form, factor, and then set each factor equal to 0. Multiplying both sides of an equation by variable factors may lead to extraneous solutions A solution that does not solve the original equation., which are solutions that do not solve the original equation. A complete list of steps for solving a rational equation is outlined in the following example. Rewrite it in standard form, factor, and then set each factor equal to 0. Always substitute into the original equation, or the factored equivalent. In the next two examples, we demonstrate two ways in which a rational equation can have no solutions. To clear the fractions, multiply by the LCD, ( x 4 ) ( x 5 ). Do not try to clear algebraic fractions when simplifying expressions. If we multiply the expression by the LCD, x ( 2 x 1 ), we obtain another expression that is not equivalent. Hence the techniques described in this section can be used to solve for particular variables. Assume that all variable expressions in the denominator are nonzero. Assuming that y is nonzero, multiply both sides by y and then add 5 to both sides. The resulting equivalent equation can be solved using the techniques learned up to this point. Therefore, we must check the solutions against the set of restrictions. If a solution is a restriction, then it is not part of the domain and is extraneous.
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