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Extra resources for Algebra II Essentials For Dummies (For Dummies (Math & Science))
Two of the most common ways to get rid of the fractions are multiplying through by the least common denominator (LCD) and cross-multiplying proportions. I just happen to discuss both of these techniques in the sections that follow. This mathematical sleight of hand — using alternate equations to solve more complicated problems — isn’t without its potential problems. At times, the new equation produces an extraneous solution (also referred to as an extraneous root), a false solution that pops up because you messed around with the original format of the equation.
In general, you deal with radicals in equations the same way you deal with fractions in equations — you get rid of them. But watch out: extraneous answers often crop up in your work, so you have to check your answers. 40 Algebra II Essentials For Dummies Squaring both sides of the equation If you have an equation with a square root term in it, you square both sides of the equation to get rid of the radical. Solve for x in . First, add 6 to both sides of the equation to get the radical by itself on the left.
When x = 2, you get 4 – 2 = 2, which isn’t bigger than 12. You can’t use x = 2 in the solution. Do you then conclude that smaller numbers don’t work? Not so. When you try x = –10, you get 100 + 10 = 110, which is most definitely bigger than 12. You can actually find infinitely many numbers that make this inequality a true statement. Chapter 3: Making Quick Work of Quadratic Equations 31 Therefore, you need to solve the inequality by using the steps I outline in the introduction to this section: 1.