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

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

Evaluate

$$\frac{7x^{2}-13x+10}{x\left(x-2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x-2}{x-2}.

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

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

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

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

$$\frac{3x+4x-8}{x-2}-\frac{5}{x}$$

Combine like terms in 3x+4x-8.

$$\frac{7x-8}{x-2}-\frac{5}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x is x\left(x-2\right). Multiply \frac{7x-8}{x-2} times \frac{x}{x}. Multiply \frac{5}{x} times \frac{x-2}{x-2}.

$$\frac{\left(7x-8\right)x}{x\left(x-2\right)}-\frac{5\left(x-2\right)}{x\left(x-2\right)}$$

Since \frac{\left(7x-8\right)x}{x\left(x-2\right)} and \frac{5\left(x-2\right)}{x\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(7x-8\right)x-5\left(x-2\right)}{x\left(x-2\right)}$$

Do the multiplications in \left(7x-8\right)x-5\left(x-2\right).

$$\frac{7x^{2}-8x-5x+10}{x\left(x-2\right)}$$

Combine like terms in 7x^{2}-8x-5x+10.

$$\frac{7x^{2}-13x+10}{x\left(x-2\right)}$$

Expand x\left(x-2\right).

$$\frac{7x^{2}-13x+10}{x^{2}-2x}$$

Differentiate w.r.t. x

$$\frac{20-20x-x^{2}}{\left(x\left(x-2\right)\right)^{2}}$$