Solve 3+x/x^2+4/2x

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

Evaluate

$$\frac{3\left(x+1\right)}{x^{2}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{6+2x+4x}{2x^{2}}$$

Combine like terms in 6+2x+4x.

$$\frac{6+6x}{2x^{2}}$$

Factor the expressions that are not already factored in \frac{6+6x}{2x^{2}}.

$$\frac{6\left(x+1\right)}{2x^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\left(x+1\right)}{x^{2}}$$

Use the distributive property to multiply 3 by x+1.

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

Expand

$$\frac{3\left(x+1\right)}{x^{2}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{6+2x+4x}{2x^{2}}$$

Combine like terms in 6+2x+4x.

$$\frac{6+6x}{2x^{2}}$$

Factor the expressions that are not already factored in \frac{6+6x}{2x^{2}}.

$$\frac{6\left(x+1\right)}{2x^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\left(x+1\right)}{x^{2}}$$

Use the distributive property to multiply 3 by x+1.

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