Question

2x/x+3 + 3/x-1 add rational expressions

Answer 1

\[\frac{ 2x }{ x+3 } + \frac{ 3 }{ x-1 }\]

Answer 2

In order to add two expressions, what has to be true about their denominators?

Answer 3

Their denominators have to be the same - like when you add two numbers normally, ie 6+3, you're really adding

\[6+3=\frac{6}{1}+\frac{3}{1}=\frac{6+3}{1}= \frac{9}{1}=9\]

Answer 4

In our case
\[ \frac{2x}{x+3}+ \frac{3}{x-1}\]
we have to somehow make the denominators the same!

To do this, all you have to remember is that any expression multiplied by 1 remains unchanged, and that any term divided by itself is 1

\[ \frac{2x}{x+3}+ \frac{3}{x-1}\]
\[=1\cdot \frac{2x}{x+3}+ 1\cdot \frac{3}{x-1}\]
\[=\frac{x-1}{x-1} \cdot \frac{2x}{x+3}+ \frac{x+3}{x+3} \cdot \frac{3}{x-1}\]
\[= \frac{(x-1)(2x)+(x+3)(3)}{(x+3)(x-1)}\]

Then you can simplify to your heart's content ^_^