EQUATIONS INVOLVING FRACTIONS (RATIONAL EQUATIONS)

Note:

• A rational equation is an equation where at least one denominator contains a variable.

• When a denominator contains a variable, there is usually a restriction on the domain. The variable cannot take on any number that would cause any denominator to be zero.

• The first step is solving a rational equation is to convert the equation to an equation without denominators. This new equation may be equivalent (same solutions as the original equation) or it may not be equivalent (extraneous solutions).

• The next step is to set the equation equal to zero and solve.

• Remember that you are trying to isolate the variable.

• Depending on the problem, there are several methods available to help you solve the problem.

If you would like an in-depth review of fractions, click on Fractions.

Solve for x in the following equation.

If you would like to see the answers and the solutions, click on solution.

Problem 5.4a:        

$$\frac{3x-7}{x^{2}-7x+6}-\displaystyle \frac{5x-5}{ x^{2}+4x-5}=\displaystyle \frac{x+20}{x^{2}-x-30}\bigskip$$

Solution

Problem 5.4b:        

$$\frac{4x-3}{2x^{2}+5x-12}+\displaystyle \frac{3}{x^{2}-16}= \displaystyle \frac{10x-11}{2x^{2}-11x+12}$$

Solution

Problem 5.4c:        

$$\frac{x-6}{\left( x-1\right) ^{2}}+\displaystyle \frac{x+3 }{\left( x-2\right) ^{2}}=\displaystyle \frac{7x^{2}+6x}{x^{4}-6x^{3}+13x^{2}-12x+4}$$

Solution

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