Solve 1/v-4*v^2-7v+12/v+3

$$\frac { 1 } { v - 4 } \cdot \frac { v ^ { 2 } - 7 v + 12 } { v + 3 }$$

Evaluate

$$\frac{v-3}{v+3}$$

Short Solution Steps

Multiply \frac{1}{v-4} times \frac{v^{2}-7v+12}{v+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{v^{2}-7v+12}{\left(v-4\right)\left(v+3\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(v-4\right)\left(v-3\right)}{\left(v-4\right)\left(v+3\right)}$$

Cancel out v-4 in both numerator and denominator.

$$\frac{v-3}{v+3}$$

Expand

$$\frac{v-3}{v+3}$$

Short Solution Steps

Multiply \frac{1}{v-4} times \frac{v^{2}-7v+12}{v+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{v^{2}-7v+12}{\left(v-4\right)\left(v+3\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(v-4\right)\left(v-3\right)}{\left(v-4\right)\left(v+3\right)}$$

Cancel out v-4 in both numerator and denominator.

$$\frac{v-3}{v+3}$$