Solve 1-q^3/1-q-3q^2

$$\frac { 1 - q ^ { 3 } } { 1 - q } - 3 q ^ { 2 }$$

Evaluate

$$1+q-2q^{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{1-q^{3}}{1-q}.

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

Extract the negative sign in -1+q.

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

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

$$-\left(-q^{2}-q-1\right)-3q^{2}$$

Expand the expression.

$$q^{2}+q+1-3q^{2}$$

Combine q^{2} and -3q^{2} to get -2q^{2}.

$$-2q^{2}+q+1$$

Expand

$$1+q-2q^{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{1-q^{3}}{1-q}.

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

Extract the negative sign in -1+q.

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

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

$$-\left(-q^{2}-q-1\right)-3q^{2}$$

Expand the expression.

$$q^{2}+q+1-3q^{2}$$

Combine q^{2} and -3q^{2} to get -2q^{2}.

$$-2q^{2}+q+1$$