Solve (1-1/1-a)*(1/a^2-1)=

$$( 1 - \frac { 1 } { 1 - a } ) \cdot ( \frac { 1 } { a ^ { 2 } } - 1 ) =$$

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in 1-a-1.

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

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

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

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

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

Multiply \frac{-a}{1-a} times \frac{1-a^{2}}{a^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a in both numerator and denominator.

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

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.

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

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

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

Expand the expression.

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

Expand

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

Short Solution Steps

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

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

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

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

Combine like terms in 1-a-1.

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

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

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

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

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

Multiply \frac{-a}{1-a} times \frac{1-a^{2}}{a^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a in both numerator and denominator.

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

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.

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

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

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

Expand the expression.

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