Hi, I am Dr. Shah, I was the National Lector Competition winner in 1989 and I am the math master at Mathscool. Now, ready for a new word in math? So, now you are going to learn solving rational equations. Rational equations are equations, where you have the fraction. So the rules for solving the rational equations are, multiply by the denominators to get rid of any fractions. So we call rational equation which have got fractions in it, so the first step we do is get rid of those fractions. Then multiply out brackets, and then collect all the terms to one side and then solve it. So to do an example, x = 3/x+2, first step is to put in some brackets around this x+2.Whenever you have a sum, a plus or minus sign inside a fraction, we need to put a bracket around it, if you want to make sure to get it right, you put those in. Multiply by denominator to get rid of the fraction. So there is a denominator of this fraction, so get rid of the fraction, we are going to multiply this by (x+2), multiply both sides by (x+2), and now divided by x+2 and multiplied by x+2, cancel each other out and so on this side, we get 'x' times (x+2) and on this side, we are just left with 3. So multiply by denominator to get rid of the fractions, we have done already. Next step is multiply out the brackets, so we are going to multiply out the brackets. x square plus 2x equals 3, x²+ 2x = 3. Collect all the terms to one side, so that 3 I want to take out to the other side, so add -3 on both the sides, they cancel out and left with 0 here. Now, it is x²+ 2x-3=0. This is now a quadratic, and so we want to factorize that quadratic, and I am going to factorize it. I know to get x², I need x times x, and to get -3, well, I could try +3 times -1, +3 times -1 give me -3. I'll just check whether that works, (x+3)(x-1)=0, is x², -1x + 3x just that gives me the +2x, which I need there, and a -3, equals 0. Once you factorize it, either this first factor is 0, in which case 'x' would have to be -3, or the second factor is 0, in which case, x would have to be 1. And that is how the rational equation is solved. .

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