Context: This is the exercise that I had to try to solve.
I couldn't figure it out and the image below is solution to this exercise.
in other words, how can this $ \frac{m}{n}= 2-\frac{3x}{x+1}$ turn into that $ 2-\frac{3x}{x+1} = \frac{2(x+1)-3x}{x+1} $
If would appreciate if you could explain to me what are the thoughts and reasonings that are involved in the process to pass from the first part of the equation to the second one. Thanks.
What I was missing is that I was not considering the common denominator between step 1 and 2 (look at picture 2)
Using common denominator is the key to figure out why this $$ \frac{m}{n}= 2-\frac{3x}{x+1}$$ turns into that $$ 2-\frac{3x}{x+1} = \frac{2(x+1)-3x}{x+1} $$
This is the link that explains how to find and use the common denominator to solve similar problems. https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:adding-and-subtracting-rational-expressions/v/algebraic-expression-adding-fractions
I hope this will help.