Solve 1+3/x/1+frac{4{x}+3/x^2}=

$$\frac { 1 + \frac { 3 } { x } } { 1 + \frac { 4 } { x } + \frac { 3 } { x ^ { 2 } } } =$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Since \frac{x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

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

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{x+4}{x} times \frac{x}{x}.

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

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

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

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

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

Divide \frac{x+3}{x} by \frac{x^{2}+4x+3}{x^{2}} by multiplying \frac{x+3}{x} by the reciprocal of \frac{x^{2}+4x+3}{x^{2}}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+3 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Since \frac{x}{x} and \frac{4}{x} have the same denominator, add them by adding their numerators.

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

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{x+4}{x} times \frac{x}{x}.

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

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

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

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

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

Divide \frac{x+3}{x} by \frac{x^{2}+4x+3}{x^{2}} by multiplying \frac{x+3}{x} by the reciprocal of \frac{x^{2}+4x+3}{x^{2}}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+3 in both numerator and denominator.

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