Solve 6v/4v^4-16v^3-3v+12/4v^4-16v^3

$$\frac { 6 v } { 4 v ^ { 4 } - 16 v ^ { 3 } } - \frac { 3 v + 12 } { 4 v ^ { 4 } - 16 v ^ { 3 } }$$

Evaluate

$$\frac{3}{4v^{3}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{6v}{4v^{4}-16v^{3}}.

$$\frac{6v}{4\left(v-4\right)v^{3}}-\frac{3v+12}{4v^{4}-16v^{3}}$$

Cancel out 2v in both numerator and denominator.

$$\frac{3}{2\left(v-4\right)v^{2}}-\frac{3v+12}{4v^{4}-16v^{3}}$$

Factor 4v^{4}-16v^{3}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(v-4\right)v^{2} and 4\left(v-4\right)v^{3} is 4\left(v-4\right)v^{3}. Multiply \frac{3}{2\left(v-4\right)v^{2}} times \frac{2v}{2v}.

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

Since \frac{3\times 2v}{4\left(v-4\right)v^{3}} and \frac{3v+12}{4\left(v-4\right)v^{3}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 2v-\left(3v+12\right).

$$\frac{6v-3v-12}{4\left(v-4\right)v^{3}}$$

Combine like terms in 6v-3v-12.

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

Factor the expressions that are not already factored in \frac{3v-12}{4\left(v-4\right)v^{3}}.

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

Cancel out v-4 in both numerator and denominator.

$$\frac{3}{4v^{3}}$$

Expand

$$\frac{3}{4v^{3}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{6v}{4v^{4}-16v^{3}}.

$$\frac{6v}{4\left(v-4\right)v^{3}}-\frac{3v+12}{4v^{4}-16v^{3}}$$

Cancel out 2v in both numerator and denominator.

$$\frac{3}{2\left(v-4\right)v^{2}}-\frac{3v+12}{4v^{4}-16v^{3}}$$

Factor 4v^{4}-16v^{3}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(v-4\right)v^{2} and 4\left(v-4\right)v^{3} is 4\left(v-4\right)v^{3}. Multiply \frac{3}{2\left(v-4\right)v^{2}} times \frac{2v}{2v}.

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

Since \frac{3\times 2v}{4\left(v-4\right)v^{3}} and \frac{3v+12}{4\left(v-4\right)v^{3}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\times 2v-\left(3v+12\right).

$$\frac{6v-3v-12}{4\left(v-4\right)v^{3}}$$

Combine like terms in 6v-3v-12.

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

Factor the expressions that are not already factored in \frac{3v-12}{4\left(v-4\right)v^{3}}.

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

Cancel out v-4 in both numerator and denominator.

$$\frac{3}{4v^{3}}$$