Solve x/x+3+1/x-4

$$\frac { x } { x + 3 } + \frac { 1 } { x } - 4$$

Evaluate

$$\frac{3-11x-3x^{2}}{x\left(x+3\right)}$$

Short Solution Steps

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

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

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

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

Do the multiplications in xx+x+3.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x\left(x+3\right)}{x\left(x+3\right)}.

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

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

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

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

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

Combine like terms in x^{2}+x+3-4x^{2}-12x.

$$\frac{-3x^{2}-11x+3}{x\left(x+3\right)}$$

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

$$\frac{-3x^{2}-11x+3}{x^{2}+3x}$$

Differentiate w.r.t. x

$$\frac{2x^{2}-6x-9}{\left(x\left(x+3\right)\right)^{2}}$$