Solve 1/x+3/x^2/frac{3{x}+1}

$$\frac { \frac { 1 } { x } + \frac { 3 } { x ^ { 2 } } } { \frac { 3 } { x } + 1 }$$

Evaluate

$$\frac{1}{x}$$

Solution Steps

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{1}{x} times \frac{x}{x}.

$$\frac{\frac{x}{x^{2}}+\frac{3}{x^{2}}}{\frac{3}{x}+1}$$

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

$$\frac{\frac{x+3}{x^{2}}}{\frac{3}{x}+1}$$

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

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

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

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

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

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

Cancel out x\left(x+3\right) in both numerator and denominator.

$$\frac{1}{x}$$

Expand

$$\frac{1}{x}$$

Solution Steps

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{1}{x} times \frac{x}{x}.

$$\frac{\frac{x}{x^{2}}+\frac{3}{x^{2}}}{\frac{3}{x}+1}$$

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

$$\frac{\frac{x+3}{x^{2}}}{\frac{3}{x}+1}$$

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

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

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

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

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

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

Cancel out x\left(x+3\right) in both numerator and denominator.

$$\frac{1}{x}$$