Solve (2a+1/a+a)diva^2-1/a

$$( \frac { 2 a + 1 } { a } + a ) \div \frac { a ^ { 2 } - 1 } { a }$$

Evaluate

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

Short Solution Steps

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

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

Since \frac{2a+1}{a} and \frac{aa}{a} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2a+1+aa.

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

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

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

Cancel out a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

Since \frac{2a+1}{a} and \frac{aa}{a} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2a+1+aa.

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

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

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

Cancel out a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a+1 in both numerator and denominator.

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