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

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

Evaluate

$$a-1$$

Short Solution Steps

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

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

Since \frac{a^{2}a}{a} and \frac{1}{a} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in a^{2}a-1.

$$\frac{\frac{a^{3}-1}{a}}{a+\frac{1}{a}+1}$$

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

$$\frac{\frac{a^{3}-1}{a}}{\frac{\left(a+1\right)a}{a}+\frac{1}{a}}$$

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

$$\frac{\frac{a^{3}-1}{a}}{\frac{\left(a+1\right)a+1}{a}}$$

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

$$\frac{\frac{a^{3}-1}{a}}{\frac{a^{2}+a+1}{a}}$$

Divide \frac{a^{3}-1}{a} by \frac{a^{2}+a+1}{a} by multiplying \frac{a^{3}-1}{a} by the reciprocal of \frac{a^{2}+a+1}{a}.

$$\frac{\left(a^{3}-1\right)a}{a\left(a^{2}+a+1\right)}$$

Cancel out a in both numerator and denominator.

$$\frac{a^{3}-1}{a^{2}+a+1}$$

Factor the expressions that are not already factored.

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

Cancel out a^{2}+a+1 in both numerator and denominator.

$$a-1$$

Expand

$$a-1$$

Short Solution Steps

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

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

Since \frac{a^{2}a}{a} and \frac{1}{a} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in a^{2}a-1.

$$\frac{\frac{a^{3}-1}{a}}{a+\frac{1}{a}+1}$$

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

$$\frac{\frac{a^{3}-1}{a}}{\frac{\left(a+1\right)a}{a}+\frac{1}{a}}$$

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

$$\frac{\frac{a^{3}-1}{a}}{\frac{\left(a+1\right)a+1}{a}}$$

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

$$\frac{\frac{a^{3}-1}{a}}{\frac{a^{2}+a+1}{a}}$$

Divide \frac{a^{3}-1}{a} by \frac{a^{2}+a+1}{a} by multiplying \frac{a^{3}-1}{a} by the reciprocal of \frac{a^{2}+a+1}{a}.

$$\frac{\left(a^{3}-1\right)a}{a\left(a^{2}+a+1\right)}$$

Cancel out a in both numerator and denominator.

$$\frac{a^{3}-1}{a^{2}+a+1}$$

Factor the expressions that are not already factored.

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

Cancel out a^{2}+a+1 in both numerator and denominator.

$$a-1$$