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 Sunday 17th of June

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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Equations That Contain Rational Expressions

Letâ€™s consider the case where some of the rational expressions have a variable in the denominator.

Example

Solve:

 Solution Multiply each side of the equation by 4x, the LCD of the rational expressions. Distribute 4x to each term on the left side. Reduce by canceling common factors. 8 + x(x - 2) = 23 Distribute x. 8 + x2 - 2x = 23 The fractions have been eliminated and we are left with the quadratic equation 8 + x2 - 2x = 23. To solve this equation, first write it in standard form, ax2 + bx + c = 0. x2 - 2x - 15 = 0 To factor x2 - 2x - 15, find two integers whose product is -15 and whose sum is -2. They are -5 and 3. Use the Zero Product Property. Solve each equation. x - 5x = 0 = 5 or or x + 3 = 0x = -3

So, the equation has two solutions: 5 and -3.

To check the solutions, we substitute each value of x in the original equation and simplify.