Question

Can anyone give me a clear example of Adding/Subtracting and simplifying rational expressions?

Answer 1

dropping out

Answer 2

Rational expressions like this?\[\large\rm \frac{1}{x^2+3x+2}+\frac{x+2}{x+1}\]

Answer 3

yes @zepdrix

Answer 4

We can at least do this example I guess,
and see if you find anything confusing.

\(\large\rm x^2+3x+2\) can be factored.

Hmm need `factors of 2` which will also `sum to 3`.
Oh oh 2*1 = 2
and 2+1 = 3.
Ok so we found our values! 2 and 1.\[\large\rm x^2+3x+2=(x+2)(x+1)\]

Answer 5

So our denominator on the left becomes,\[\large\rm \frac{1}{(x+2)(x+1)}+\frac{x+2}{x+1}\]

Answer 6

We need a common denominator,
notice the denominators already share something in common,\[\large\rm \frac{1}{(x+2)\color{orange}{(x+1)}}+\frac{x+2}{\color{orange}{(x+1)}}\]

Answer 7

So it appears our second fraction needs an (x+2),
both in numerator and denominator,\[\large\rm \frac{1}{(x+2)\color{orange}{(x+1)}}+\frac{x+2}{\color{orange}{(x+1)}}\frac{(x+2)}{(x+2)}\]

Answer 8

From here, since they have the same denominator,
we can rewrite this as a single fraction,\[\large\rm \frac{1+(x+2)(x+2)}{(x+2)(x+1)}\]

Answer 9

And simplify from there.
What do you think?
Confusing? :d

Answer 10

Not really, that helped a lot, thank you!