Solve 9/x^2+3/x/frac{9{x}+3/x^2}

$$\frac { \frac { 9 } { x ^ { 2 } } + \frac { 3 } { x } } { \frac { 9 } { x } + \frac { 3 } { x ^ { 2 } } }$$

Evaluate

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

Short Solution Steps

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

$$\frac{\frac{9}{x^{2}}+\frac{3x}{x^{2}}}{\frac{9}{x}+\frac{3}{x^{2}}}$$

Since \frac{9}{x^{2}} and \frac{3x}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+3x}{x^{2}}}{\frac{9}{x}+\frac{3}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{9}{x} times \frac{x}{x}.

$$\frac{\frac{9+3x}{x^{2}}}{\frac{9x}{x^{2}}+\frac{3}{x^{2}}}$$

Since \frac{9x}{x^{2}} and \frac{3}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+3x}{x^{2}}}{\frac{9x+3}{x^{2}}}$$

Divide \frac{9+3x}{x^{2}} by \frac{9x+3}{x^{2}} by multiplying \frac{9+3x}{x^{2}} by the reciprocal of \frac{9x+3}{x^{2}}.

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

Cancel out x^{2} in both numerator and denominator.

$$\frac{3x+9}{9x+3}$$

Factor the expressions that are not already factored.

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

Cancel out 3 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

$$\frac{\frac{9}{x^{2}}+\frac{3x}{x^{2}}}{\frac{9}{x}+\frac{3}{x^{2}}}$$

Since \frac{9}{x^{2}} and \frac{3x}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+3x}{x^{2}}}{\frac{9}{x}+\frac{3}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{9}{x} times \frac{x}{x}.

$$\frac{\frac{9+3x}{x^{2}}}{\frac{9x}{x^{2}}+\frac{3}{x^{2}}}$$

Since \frac{9x}{x^{2}} and \frac{3}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+3x}{x^{2}}}{\frac{9x+3}{x^{2}}}$$

Divide \frac{9+3x}{x^{2}} by \frac{9x+3}{x^{2}} by multiplying \frac{9+3x}{x^{2}} by the reciprocal of \frac{9x+3}{x^{2}}.

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

Cancel out x^{2} in both numerator and denominator.

$$\frac{3x+9}{9x+3}$$

Factor the expressions that are not already factored.

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

Cancel out 3 in both numerator and denominator.

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