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-2x/x+6+5=-x/x+6

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1 Answer

This problem is called a rational equation because the Xs are in the deminators of the fractions. To solve a rational equation, you have to find the common denominator, just like you do when you add or subtract normal fractions. Here, the common denominator is X+6 because two of the fractions have that denominator, and the third one, the 5, has a denominator of 1, which can go into anything. Once you have figured out what the common denominator is, multiply each term by the common denominator. So, in this case, you would multiply 2x/(x+6), 5, and -x/(x+6) each by (x+6). In the first term and the last term the (x+6) would cancel out on the top and bottom to leave you what was orginally in the numerator, -2x and -x. In the case of the 5, you need to distribute it to the (x+6) to get 5x+30. Your equation should now look like this: -2x +5x+30 = -x. You can then simplify and solve this like a normal linear equation. First, combine like terms on the left to get 3x + 30 =-x. Then, subtract 3x from both sides to get 30 = -4x. Finally, divide both sides by -4 to get x = -15/2. You can always check your asnwer by substituting it in for x in the original to see if you get the same number on both sides of the equal sign. 

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