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

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

Evaluate

$$\frac{2x^{2}+7x-11}{x\left(x+3\right)\left(x+5\right)}$$

Short Solution Steps

Factor x^{2}+5x. Factor x^{2}+3x.

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

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

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

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

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

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

$$\frac{x^{2}+3x+3x+9+x^{2}+5x-4x-20}{x\left(x+3\right)\left(x+5\right)}$$

Combine like terms in x^{2}+3x+3x+9+x^{2}+5x-4x-20.

$$\frac{2x^{2}+7x-11}{x\left(x+3\right)\left(x+5\right)}$$

Expand x\left(x+3\right)\left(x+5\right).

$$\frac{2x^{2}+7x-11}{x^{3}+8x^{2}+15x}$$

Expand

$$\frac{2x^{2}+7x-11}{x\left(x+3\right)\left(x+5\right)}$$

Short Solution Steps

Factor x^{2}+5x. Factor x^{2}+3x.

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

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

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

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

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

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

$$\frac{x^{2}+3x+3x+9+x^{2}+5x-4x-20}{x\left(x+3\right)\left(x+5\right)}$$

Combine like terms in x^{2}+3x+3x+9+x^{2}+5x-4x-20.

$$\frac{2x^{2}+7x-11}{x\left(x+3\right)\left(x+5\right)}$$

Expand x\left(x+3\right)\left(x+5\right).

$$\frac{2x^{2}+7x-11}{x^{3}+8x^{2}+15x}$$