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

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

Evaluate

$$x+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.

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

Since \frac{x+2}{x+2} and \frac{3}{x+2} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in x+2-3.

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

$$x+2$$

Expand

$$x+2$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.

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

Since \frac{x+2}{x+2} and \frac{3}{x+2} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in x+2-3.

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

$$x+2$$