Math Problem Solver

Simplified:

$$\frac{14}{3 x - 21} + \frac{x + 4}{\frac{2 {x}^{2} - 6 x - 56}{2 x + 3}} = \frac{x + \frac{37}{6}}{x - 7}$$

$$\begin{aligned}\frac{x + 4}{\frac{2 x^{2} - 6 x - 56}{2 x + 3}} + \frac{14}{3 x - 21}&=\frac{\left(2 x + 3\right) \left(x + 4\right)}{2 x^{2} - 6 x - 56} + \frac{14}{3 x - 21}\\&=\frac{14}{3 x - 21} + \frac{2 x + 3}{2 x - 14}\\&=\frac{\frac{14 \cdot \left(2 x - 14\right)}{3 x - 21}}{2 x - 14} + \frac{\frac{\left(2 x + 3\right) \left(3 x - 21\right)}{2 x - 14}}{3 x - 21}\\&=\frac{x + \frac{37}{6}}{x - 7}\end{aligned}$$

Expanded:

$$\frac{14}{3 x - 21} + \frac{x + 4}{\frac{2 {x}^{2} - 6 x - 56}{2 x + 3}} = \frac{x}{\frac{2 x^{2}}{2 x + 3} - \frac{6 x}{2 x + 3} - \frac{56}{2 x + 3}} + \frac{4}{\frac{2 x^{2}}{2 x + 3} - \frac{6 x}{2 x + 3} - \frac{56}{2 x + 3}} + \frac{14}{3 x - 21}$$

Factored:

$$\frac{14}{3 x - 21} + \frac{x + 4}{\frac{2 {x}^{2} - 6 x - 56}{2 x + 3}} = \frac{6 x + 37}{6 \left(x - 7\right)}$$