Solve x^3-2x/3x+2+(1+2/x-4)

$$\frac { x ^ { 3 } - 2 x } { 3 x + 2 } + ( 1 + \frac { 2 } { x - 4 } )$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3x+2}{3x+2}.

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

Since \frac{x^{3}-2x}{3x+2} and \frac{3x+2}{3x+2} have the same denominator, add them by adding their numerators.

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

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

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

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

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

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

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

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

$$\frac{x^{4}-4x^{3}+x^{2}-4x+2x-8+6x+4}{\left(x-4\right)\left(3x+2\right)}$$

Combine like terms in x^{4}-4x^{3}+x^{2}-4x+2x-8+6x+4.

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

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

$$\frac{x^{4}-4x^{3}+x^{2}+4x-4}{3x^{2}-10x-8}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3x+2}{3x+2}.

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

Since \frac{x^{3}-2x}{3x+2} and \frac{3x+2}{3x+2} have the same denominator, add them by adding their numerators.

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

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

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

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

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

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

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

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

$$\frac{x^{4}-4x^{3}+x^{2}-4x+2x-8+6x+4}{\left(x-4\right)\left(3x+2\right)}$$

Combine like terms in x^{4}-4x^{3}+x^{2}-4x+2x-8+6x+4.

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

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

$$\frac{x^{4}-4x^{3}+x^{2}+4x-4}{3x^{2}-10x-8}$$