#### Answer

$$\frac{-27x+44}{\left(x+1\right)\left(3x-4\right)}$$

#### Work Step by Step

In order to simplify the expression, we first must create like denominators. After ensuring that the denominators are like denominators, we can simplify the fractions. Thus, we find:
$$\frac{8}{\left(x+1\right)\left(3x-4\right)}-\frac{9}{x+1} \\ \frac{8}{\left(x+1\right)\left(3x-4\right)}-\frac{9\left(3x-4\right)}{\left(x+1\right)\left(3x-4\right)} \\ \frac{8-9\left(3x-4\right)}{\left(x+1\right)\left(3x-4\right)} \\ \frac{-27x+44}{\left(x+1\right)\left(3x-4\right)}$$