This week in math we learned about solving rational equations. When solving rational equations there are a few ways to do it, you could move all the variables to one side, for example if you were given the equation \frac{5}{x} + 2 = \frac{3}{x}, you could move the terms with x to the left, and bring the numbers to the right, making the fraction \frac{5}{x} – \frac{3}{x} = -2, from there because the fractions have same denominator, you can add the two together, making the fraction \frac{2}{x} = \frac{-2}{1}. This is when you can cross multiply because it is a fraction=another fraction, turning the fraction into -2x = 2, you would then use algebra and divide -2 from both sides giving you x = -1. The picture bellow is of what I just went over:

With some equations the best way to solve it is to multiply by a common denominator, for example if you were given the equation \frac{5x - 2}{(x + 2)} – \frac{2x - 1}{(x - 3)} = 3, you would multiply by the common denominator which is (x + 2)(x – 3), and you would cross out top and bottom terms that are the same within the same fraction giving you      (x – 3)(5x – 2) – (x + 2)(2x – 1) = 3(x + 2)(x – 3), you would then use algebra to get to the final answer of x = \frac{26}{17}. The picture bellow is of what I just went over: