Solve x+3/x+1+3(x+3)/x+1/frac{x+3{x+1}+x+1/x+1}

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

Evaluate

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

Short Solution Steps

Divide x+1 by x+1 to get 1.

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

Since \frac{x+3}{x+1} and \frac{3\left(x+3\right)}{x+1} have the same denominator, add them by adding their numerators.

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

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

$$\frac{\frac{x+3+3x+9}{x+1}}{\frac{x+3}{x+1}+1}$$

Combine like terms in x+3+3x+9.

$$\frac{\frac{4x+12}{x+1}}{\frac{x+3}{x+1}+1}$$

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

$$\frac{\frac{4x+12}{x+1}}{\frac{x+3}{x+1}+\frac{x+1}{x+1}}$$

Since \frac{x+3}{x+1} and \frac{x+1}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x+12}{x+1}}{\frac{x+3+x+1}{x+1}}$$

Combine like terms in x+3+x+1.

$$\frac{\frac{4x+12}{x+1}}{\frac{2x+4}{x+1}}$$

Divide \frac{4x+12}{x+1} by \frac{2x+4}{x+1} by multiplying \frac{4x+12}{x+1} by the reciprocal of \frac{2x+4}{x+1}.

$$\frac{\left(4x+12\right)\left(x+1\right)}{\left(x+1\right)\left(2x+4\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{4x+12}{2x+4}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

Divide x+1 by x+1 to get 1.

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

Since \frac{x+3}{x+1} and \frac{3\left(x+3\right)}{x+1} have the same denominator, add them by adding their numerators.

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

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

$$\frac{\frac{x+3+3x+9}{x+1}}{\frac{x+3}{x+1}+1}$$

Combine like terms in x+3+3x+9.

$$\frac{\frac{4x+12}{x+1}}{\frac{x+3}{x+1}+1}$$

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

$$\frac{\frac{4x+12}{x+1}}{\frac{x+3}{x+1}+\frac{x+1}{x+1}}$$

Since \frac{x+3}{x+1} and \frac{x+1}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x+12}{x+1}}{\frac{x+3+x+1}{x+1}}$$

Combine like terms in x+3+x+1.

$$\frac{\frac{4x+12}{x+1}}{\frac{2x+4}{x+1}}$$

Divide \frac{4x+12}{x+1} by \frac{2x+4}{x+1} by multiplying \frac{4x+12}{x+1} by the reciprocal of \frac{2x+4}{x+1}.

$$\frac{\left(4x+12\right)\left(x+1\right)}{\left(x+1\right)\left(2x+4\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{4x+12}{2x+4}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

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