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

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

Evaluate

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

Short Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

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

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

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

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

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

Do the multiplications in aa-1.

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

Calculate a to the power of 1 and get a.

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

Express \frac{\frac{a^{2}-1}{a}}{1-a} as a single fraction.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+a.

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

Cancel out -a+1 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

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

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

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

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

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

Do the multiplications in aa-1.

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

Calculate a to the power of 1 and get a.

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

Express \frac{\frac{a^{2}-1}{a}}{1-a} as a single fraction.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+a.

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

Cancel out -a+1 in both numerator and denominator.

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

Expand the expression.

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