# Solving rational equations 2 | Polynomial and rational functions | Algebra II | Khan Academy

Solve the following equation 5 / 2x – 4 / 3x = 7/18 And we gave that x cannot be equal to 0, because that is It will make these two statements anonymous I hope the answer here is not 0, and then that becomes – This is additional information that is not needed– So let’s find how to solve it A good place to start – I prefer not to have x statements in The Maqam So let’s hit – and in fact, generally no better There are fractions in the equations that I solve– So let’s see if we can hit both ends of this Equation with objects in which fractions are eliminated Let me rewrite it so we get some space 5 / 2x, and then we have -4 / 3x = 7/18 Now, if we want to get rid of the 2 in the denominator here We can multiply everything by 2 If we want to get rid of these 3 in the place, then we can We multiply everything by 3 If we want to get rid of these 18 in the place We can multiply everything by 18 And 18 also contains 2 and 3 An analysis of 18 to its fundamental factors is 2 x 9 Ie 3 x 3 When we multiply both sides of the equation With 18, we actually multiply by 2 and 3 And 3 more So let’s multiply both sides of this equation by 18 I will multiply this phrase by 18 Then multiply that phrase by 18 This will get me rid of these numbers in The maqam 18 ÷ 3 = 6 18 ÷ 2 = 9 But we not only have numbers in the denominator, but also We have these x expressions in the denominator So let’s also multiply both sides of the equation by x This will rid us of this We will hit both ends 18x equation We take the least common multiple For 2x, 3x and 18 This is the smallest number divisible by all These three parts Now, when we do this, our maqams will disappear x ÷ x = 1 18 ÷ 2 = 9 So this phrase becomes 9 x 5, i.e. 45 Then this phrase here, x ÷ x = 1 18 ÷ 3 = 6 So we have 6 x 4 = 24, but we have a minus sign Here, then -24 = – Let me write this In yellow– = – then we have this phrase 7/18 x 18x Well, the 18 is omitted and we’ve got 7 x x = 7x Now this becomes a much simpler equation Now, what is the output of 45 – 24? Let’s see, 45 – 20 = 25 Then we subtract 4 from it, so the result is 21 So we get 21 = 7x Divide both sides by 7 and get x = 3 x = 3 And let’s check that this works So we have 5/2x This equals 5/2 x 3 – 4 / 3 x 3 This equals 5/6 – 4/18 – sorry – 4/9 We need to find a common denominator 18 is the lowest common multiple of 6 and 9, so let’s We put it over 18 5/6 is equivalent to 15/18 Multiply the numerator and denominator by 3 4/9 equals 8/18 Multiply the numerator and denominator by 2 15 – 8 So this equals 15-8, i.e. Equals 7/18 He succeeded, then 5 / 2x when x = 3, – 4 / 3x when x = 3, this is really 7/18 And with that we have finished .