\dfrac{9}{(6x+11)(x+3)}-\dfrac{3x}{(3x+10)(x+3)}=
You asked:
Evaluate the expression: \(\frac{9}{\left(6 x + 11\right) \cdot \left(x + 3\right)} - \frac{3 x}{\left(3 x + 10\right) \cdot \left(x + 3\right)}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{9}{\left(6 x + 11\right) \cdot \left(x + 3\right)} - \frac{3 x}{\left(3 x + 10\right) \cdot \left(x + 3\right)} = - \frac{3 x}{\left(3 x + 10\right) \left(x + 3\right)} + \frac{9}{\left(6 x + 11\right) \left(x + 3\right)} \)
Expanded
\[\frac{9}{\left(6 x + 11\right) \cdot \left(x + 3\right)} - \frac{3 x}{\left(3 x + 10\right) \cdot \left(x + 3\right)} = - \frac{3 x}{3 x^{2} + 19 x + 30} + \frac{9}{6 x^{2} + 29 x + 33}\]
Factored
\[\frac{9}{\left(6 x + 11\right) \cdot \left(x + 3\right)} - \frac{3 x}{\left(3 x + 10\right) \cdot \left(x + 3\right)} = - \frac{6 \cdot \left(3 x^{2} + x - 15\right)}{\left(3 x + 10\right) \left(6 x + 11\right) \left(x + 3\right)}\]