Solve (1+3/x-1)divx^2+4x+4/2x-2

$$( 1 + \frac { 3 } { x - 1 } ) \div \frac { x ^ { 2 } + 4 x + 4 } { 2 x - 2 }$$

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in x-1+3.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out \left(x-1\right)\left(x+2\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Combine like terms in x-1+3.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out \left(x-1\right)\left(x+2\right) in both numerator and denominator.

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