Solve 24/x-3+15/3x+1

$$\frac{24}{x-3} + \frac{15}{3x+1}$$

Evaluate

$$\frac{3\left(29x-7\right)}{\left(x-3\right)\left(3x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and 3x+1 is \left(x-3\right)\left(3x+1\right). Multiply \frac{24}{x-3} times \frac{3x+1}{3x+1}. Multiply \frac{15}{3x+1} times \frac{x-3}{x-3}.

$$\frac{24\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)}+\frac{15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}$$

Since \frac{24\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)} and \frac{15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{24\left(3x+1\right)+15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}$$

Do the multiplications in 24\left(3x+1\right)+15\left(x-3\right).

$$\frac{72x+24+15x-45}{\left(x-3\right)\left(3x+1\right)}$$

Combine like terms in 72x+24+15x-45.

$$\frac{87x-21}{\left(x-3\right)\left(3x+1\right)}$$

Expand \left(x-3\right)\left(3x+1\right).

$$\frac{87x-21}{3x^{2}-8x-3}$$

Factor

$$\frac{3\left(29x-7\right)}{\left(x-3\right)\left(3x+1\right)}$$