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By Mary Jane Sterling

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To guard against including extraneous solutions in your answers, you need to check the solutions you come up with in the original equations. Making your least common denominator work for you You can solve many rational equations by simply getting rid of all the denominators (which gets rid of the fractions). To do so, you introduce the LCD into the problem. The LCD is the smallest number that all the denominators in the problem divide into evenly (such as 2, 3, and 4 all dividing the LCD 12 evenly).

You end up with: The first equation has no solution. The fraction with 1 in the numerator and x3 in the denominator is never equal to 0. The only way a fraction is equal to 0 is if the numerator is 0 (and the denominator is some other number). 3. Check your answers. The only solution for this equation is dandy answer. — a perfectly 44 Algebra II Essentials For Dummies Solving quadratic-like trinomials Trinomials are expressions with three terms, with the highest term raised to the second degree, the expression is quadratic.

When x – 5 = 0, x = 5, and when x + 3 = 0, x = –3. Solve 24x2 + 52x – 112 = 0 for x. Chapter 3: Making Quick Work of Quadratic Equations 27 It may not be immediately apparent how you should factor such a seemingly complicated trinomial. But factoring 4 out of each term to simplify the picture a bit, you get 4(6x2 +13x – 28) = 0. Factoring the quadratic in the parentheses: 4(3x – 4)(2x + 7) = 0. or . Setting the two binomials equal to 0, you get The Quadratic Formula to the Rescue The quadratic formula is a wonderful tool to use when other factoring methods fail (see the previous section).

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