Solve 3x/2-5x-5/3-4x=

$$\frac { 3 x } { 2 - 5 x } - \frac { 5 } { 3 - 4 x } =$$

Evaluate

$$\frac{2\left(1-3x\right)\left(2x-5\right)}{\left(3-4x\right)\left(2-5x\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2-5x and 3-4x is \left(-5x+2\right)\left(-4x+3\right). Multiply \frac{3x}{2-5x} times \frac{-4x+3}{-4x+3}. Multiply \frac{5}{3-4x} times \frac{-5x+2}{-5x+2}.

$$\frac{3x\left(-4x+3\right)}{\left(-5x+2\right)\left(-4x+3\right)}-\frac{5\left(-5x+2\right)}{\left(-5x+2\right)\left(-4x+3\right)}$$

Since \frac{3x\left(-4x+3\right)}{\left(-5x+2\right)\left(-4x+3\right)} and \frac{5\left(-5x+2\right)}{\left(-5x+2\right)\left(-4x+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x\left(-4x+3\right)-5\left(-5x+2\right)}{\left(-5x+2\right)\left(-4x+3\right)}$$

Do the multiplications in 3x\left(-4x+3\right)-5\left(-5x+2\right).

$$\frac{-12x^{2}+9x+25x-10}{\left(-5x+2\right)\left(-4x+3\right)}$$

Combine like terms in -12x^{2}+9x+25x-10.

$$\frac{-12x^{2}+34x-10}{\left(-5x+2\right)\left(-4x+3\right)}$$

Expand \left(-5x+2\right)\left(-4x+3\right).

$$\frac{-12x^{2}+34x-10}{20x^{2}-23x+6}$$

Differentiate w.r.t. x

$$\frac{2\left(-202x^{2}+128x-13\right)}{400x^{4}-920x^{3}+769x^{2}-276x+36}$$