9.6 Solving Rational Equations

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Presentation transcript:

9.6 Solving Rational Equations p.569

Short Cut! When there is only fraction on each side of the equal sign, just cross-multiply as if you are solving a proportion.

Example: Solve. Check your solutions!

Example: Solve. Check your solutions!

Hint for solving: One method to solve a rational equation is to multiply everything through by the LCD. This will get rid of all the fractions! Beware of extraneous solutions!

Multiply each fraction through by the LCD Example: Solve. LCD: 2x Multiply each fraction through by the LCD Check your solution!

Solve. LCD: ? LCD: (x+1) ? Check your solution! No Solution!

Solve. Factor 1st! LCD: (x+2)(x-2) Check your solutions!

Here is another example that we will do together:

Step 1: Find the LCD This denominator can be factored into 3(x-2) Hint: Factor the denominator This denominator can be factored into 3(x-2) But you need at least a 6 from the other denominator Therefore….

Step 2: Multiply both sides of equation by LCD Step 2: Multiply both sides of equation by LCD. This eliminates the fractions when you cancel the matching factors.

Step 3: Solve for x

Since there are two answers, there need to be two checks. Let x =

Check #2: Let x = 2 When you check the number 2, you get a zero in the denominator. This means that 2 can not be a solution.

Now, you do these on your own.