Solve 2-2/a+1/2+frac{2{a}}=

$$\frac { 2 - \frac { 2 } { a + 1 } } { 2 + \frac { 2 } { a } } =$$

Evaluate

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

Short Solution Steps

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

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

Since \frac{2\left(a+1\right)}{a+1} and \frac{2}{a+1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\left(a+1\right)-2.

$$\frac{\frac{2a+2-2}{a+1}}{2+\frac{2}{a}}$$

Combine like terms in 2a+2-2.

$$\frac{\frac{2a}{a+1}}{2+\frac{2}{a}}$$

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

$$\frac{\frac{2a}{a+1}}{\frac{2a}{a}+\frac{2}{a}}$$

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

$$\frac{\frac{2a}{a+1}}{\frac{2a+2}{a}}$$

Divide \frac{2a}{a+1} by \frac{2a+2}{a} by multiplying \frac{2a}{a+1} by the reciprocal of \frac{2a+2}{a}.

$$\frac{2aa}{\left(a+1\right)\left(2a+2\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{a^{2}}{a^{2}+2a+1}$$

Expand

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

Short Solution Steps

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

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

Since \frac{2\left(a+1\right)}{a+1} and \frac{2}{a+1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2\left(a+1\right)-2.

$$\frac{\frac{2a+2-2}{a+1}}{2+\frac{2}{a}}$$

Combine like terms in 2a+2-2.

$$\frac{\frac{2a}{a+1}}{2+\frac{2}{a}}$$

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

$$\frac{\frac{2a}{a+1}}{\frac{2a}{a}+\frac{2}{a}}$$

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

$$\frac{\frac{2a}{a+1}}{\frac{2a+2}{a}}$$

Divide \frac{2a}{a+1} by \frac{2a+2}{a} by multiplying \frac{2a}{a+1} by the reciprocal of \frac{2a+2}{a}.

$$\frac{2aa}{\left(a+1\right)\left(2a+2\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 2 in both numerator and denominator.

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

Expand the expression.

$$\frac{a^{2}}{a^{2}+2a+1}$$