Solve v^2-4/9v+18div3v^2-12v+12/27v+54

$$\frac { v ^ { 2 } - 4 } { 9 v + 18 } \div \frac { 3 v ^ { 2 } - 12 v + 12 } { 27 v + 54 }$$

Evaluate

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

Short Solution Steps

Divide \frac{v^{2}-4}{9v+18} by \frac{3v^{2}-12v+12}{27v+54} by multiplying \frac{v^{2}-4}{9v+18} by the reciprocal of \frac{3v^{2}-12v+12}{27v+54}.

$$\frac{\left(v^{2}-4\right)\left(27v+54\right)}{\left(9v+18\right)\left(3v^{2}-12v+12\right)}$$

Factor the expressions that are not already factored.

$$\frac{27\left(v-2\right)\left(v+2\right)^{2}}{3\times 9\left(v+2\right)\left(v-2\right)^{2}}$$

Cancel out 3\times 9\left(v-2\right)\left(v+2\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide \frac{v^{2}-4}{9v+18} by \frac{3v^{2}-12v+12}{27v+54} by multiplying \frac{v^{2}-4}{9v+18} by the reciprocal of \frac{3v^{2}-12v+12}{27v+54}.

$$\frac{\left(v^{2}-4\right)\left(27v+54\right)}{\left(9v+18\right)\left(3v^{2}-12v+12\right)}$$

Factor the expressions that are not already factored.

$$\frac{27\left(v-2\right)\left(v+2\right)^{2}}{3\times 9\left(v+2\right)\left(v-2\right)^{2}}$$

Cancel out 3\times 9\left(v-2\right)\left(v+2\right) in both numerator and denominator.

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