. Simplify the following rational expressions.
2 - 3
X -1 x+1
2x² + 7x +3
2x² - 7x - 4
2x + 5 + x + 1
x² + 6x + 9 x² - 9 x - 3
For most problems like this, you just have to combine like terms.
I'm assuming here you want to factor the expressions.
Note that the roots of $\displaystyle ax^2 + bx + c$, where a, b, and c are integers, must be factors of c divided by factors of a.
To factor, you have to use this knowledge to your advantage and try different factors. Recognize that $\displaystyle 2x^2 + 7x + 3$ must factor to $\displaystyle (2x + p)(x + q)$, and we have that $\displaystyle 2x^2 + 7x + 3 = 2x^2 + (p + 2q)x + pq$. So $\displaystyle p + 2q = 7$ and $\displaystyle pq = 3$. You should be able to see relatively quickly that p = 1 and q = 3, which gives you a factorization of $\displaystyle (2x + 1)(x + 3)$. Can you do the other factorization problem?