Solve 2/a+a^2-2a/1+a=

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

Evaluate

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

Short Solution Steps

Factor a+a^{2}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a\left(a+1\right) and 1+a is a\left(a+1\right). Multiply \frac{2a}{1+a} times \frac{a}{a}.

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

Since \frac{2}{a\left(a+1\right)} and \frac{2aa}{a\left(a+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2-2aa.

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

Factor the expressions that are not already factored in \frac{2-2a^{2}}{a\left(a+1\right)}.

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

Extract the negative sign in -1-a.

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

Cancel out a+1 in both numerator and denominator.

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

Use the distributive property to multiply -2 by a-1.

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

Factor

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