Solve 3/3x-4-5/5x+6

$$\frac { 3 } { 3 x - 4 } - \frac { 5 } { 5 x + 6 }$$

Evaluate

$$\frac{38}{\left(3x-4\right)\left(5x+6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x-4 and 5x+6 is \left(3x-4\right)\left(5x+6\right). Multiply \frac{3}{3x-4} times \frac{5x+6}{5x+6}. Multiply \frac{5}{5x+6} times \frac{3x-4}{3x-4}.

$$\frac{3\left(5x+6\right)}{\left(3x-4\right)\left(5x+6\right)}-\frac{5\left(3x-4\right)}{\left(3x-4\right)\left(5x+6\right)}$$

Since \frac{3\left(5x+6\right)}{\left(3x-4\right)\left(5x+6\right)} and \frac{5\left(3x-4\right)}{\left(3x-4\right)\left(5x+6\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(5x+6\right)-5\left(3x-4\right)}{\left(3x-4\right)\left(5x+6\right)}$$

Do the multiplications in 3\left(5x+6\right)-5\left(3x-4\right).

$$\frac{15x+18-15x+20}{\left(3x-4\right)\left(5x+6\right)}$$

Combine like terms in 15x+18-15x+20.

$$\frac{38}{\left(3x-4\right)\left(5x+6\right)}$$

Expand \left(3x-4\right)\left(5x+6\right).

$$\frac{38}{15x^{2}-2x-24}$$

Differentiate w.r.t. x

$$\frac{76\left(1-15x\right)}{\left(\left(3x-4\right)\left(5x+6\right)\right)^{2}}$$