1. ## Fraction Problem

Man I dislike these fractions but I am having problems finding the answer to this one. $\displaystyle \frac{5}{2x}-\frac{4}{2x^2+3x}$

The site helps me a lot and I haven't found a math site that has help me as much as this one. Even if i am just reading someone threads or doing mine I find help in it somewheres.

2. Originally Posted by Itsbaxagain
Man I dislike these fractions but I am having problems finding the answer to this one. $\displaystyle \frac{5}{2x}-\frac{4}{2x^2+3x}$

The site helps me a lot and I haven't found a math site that has help me as much as this one. Even if i am just reading someone threads or doing mine I find help in it somewheres.
Are you supposed to subtract the fractions?

You need a common denominator. Note that the denominator of the second term is $\displaystyle 2x^2 + 3x = x(2x + 3)$. The LCM of $\displaystyle x$ and $\displaystyle x(2x + 3)$ is $\displaystyle 2x(2x + 3)$.

So....
$\displaystyle \frac{5}{2x} - \frac{4}{2x^2+3x}$

$\displaystyle = \frac{5}{2x} \cdot \frac{2x + 3}{2x + 3} - \frac{4}{2x^2+3x} \cdot \frac{2}{2}$

$\displaystyle = \frac{5(2x + 3) - 2 \cdot 4}{2x(2x + 3)}$

$\displaystyle = \frac{10x + 7}{2x(2x + 3)}$

-Dan