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 Depdendent Variable

 Number of equations to solve: 23456789
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 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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# Solving Equations Containing Rational Expressions

Example 1

Solve:

Solution

 Step 1 Find the LCD. LCD = 2 Â· 3 Â· x = 6x Step 2 Multiply by the LCD. Step 3 Distribute on the right side. Step 4 Reduce. Step 5 Solve. Simplify. Subtract 27 from both sides. Multiply both sides by -1. 18 = 27 - x-9 = -x 9 = x Step 6 Check the solution. We leave the check to you. Thus, the solution is x = 9.

Note:

Hereâ€™s one way to find the LCD of

â€¢ Factor each denominator:

x = x

2x = 2 Â· x

6 = 2 Â· 3

â€¢ List each factor the greatest number of times it appears in any factorization. x, 2, 3

â€¢ Multiply. 2 Â· 3 Â· x = 6x

So, the LCD is 6x.

Example 2

Solve:

Solution

 Step 1 Find the LCD. LCD = (x - 5)(x + 5) Step 2 Multiply by the LCD. Step 3 Distribute the LCD to both terms the right side. Step 4 Reduce. Step 5 Solve. Simplify. Distribute on the right side. Combine like terms. Add 5 to both sides. Divide both sides by 3. 16 16 16 21 7 = x + 5 + (x - 5) Â· 2 = x + 5 + 2x - 10 = 3x - 5 = 3x = x Step 6 Check the solution. We leave the check to you.
Thus, the solution is x = 7.