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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Factor the expressions that are not already factored.

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

Extract the negative sign in 1-a.

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

Cancel out a-1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Factor the expressions that are not already factored.

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

Extract the negative sign in 1-a.

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

Cancel out a-1 in both numerator and denominator.

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