In order to add and/or subtract or subtract and/or add rational expressions with different terms in the denominator, you need to find the LCM of those different terms.
Next, you want to create new denominators which are the LCM, but to make them you must multiply each term, top and bottom, by something (certain terms in the LCM) that will create the new denominators.
\(\dfrac{1}{(x - 1)} + \dfrac{3}{(x - 1)^{2}} + \dfrac{10}{3x}\)What's the added result of these rational expressions?
\(\dfrac{1}{(x - 1)} + \dfrac{3}{(x - 1)^{2}} + \dfrac{10}{3x}\)
\(LCM = (x - 1)^{2}(3x)\)
\(\dfrac{1}{(x - 1)} * \dfrac{(x - 1)}{(x - 1)} + \dfrac{3}{(x - 1)^{2}} * \dfrac{3x}{3x} + \dfrac{10}{3x} * \dfrac{(x - 1)^{2}}{(x - 1)^{2}}\)
\(\dfrac{x - 1}{ (x - 1)^{2}(3x)} + \dfrac{9x}{ (x - 1)^{2}(3x)} + \dfrac{10x^{2} - 40x + 40}{ (x - 1)^{2}(3x)} = \)
\(\dfrac{10x^{2} + 50x - 41}{ (x - 1)^{2}(3x)}\)
