Solve 1-6m/1-m^3-5/m^3-1

$$\frac { 1 - 6 m } { 1 - m ^ { 3 } } - \frac { 5 } { m ^ { 3 } - 1 }$$

Evaluate

$$\frac{6}{m^{2}+m+1}$$

Short Solution Steps

Factor 1-m^{3}. Factor m^{3}-1.

$$\frac{1-6m}{\left(m-1\right)\left(-m^{2}-m-1\right)}-\frac{5}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-1\right)\left(-m^{2}-m-1\right) and \left(m-1\right)\left(m^{2}+m+1\right) is \left(m-1\right)\left(m^{2}+m+1\right). Multiply \frac{1-6m}{\left(m-1\right)\left(-m^{2}-m-1\right)} times \frac{-1}{-1}.

$$\frac{-\left(1-6m\right)}{\left(m-1\right)\left(m^{2}+m+1\right)}-\frac{5}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

Since \frac{-\left(1-6m\right)}{\left(m-1\right)\left(m^{2}+m+1\right)} and \frac{5}{\left(m-1\right)\left(m^{2}+m+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\left(1-6m\right)-5}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

Do the multiplications in -\left(1-6m\right)-5.

$$\frac{-1+6m-5}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

Combine like terms in -1+6m-5.

$$\frac{-6+6m}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

Factor the expressions that are not already factored in \frac{-6+6m}{\left(m-1\right)\left(m^{2}+m+1\right)}.

$$\frac{6\left(m-1\right)}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

Cancel out m-1 in both numerator and denominator.

$$\frac{6}{m^{2}+m+1}$$

Expand

$$\frac{6}{m^{2}+m+1}$$

Short Solution Steps

Factor 1-m^{3}. Factor m^{3}-1.

$$\frac{1-6m}{\left(m-1\right)\left(-m^{2}-m-1\right)}-\frac{5}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-1\right)\left(-m^{2}-m-1\right) and \left(m-1\right)\left(m^{2}+m+1\right) is \left(m-1\right)\left(m^{2}+m+1\right). Multiply \frac{1-6m}{\left(m-1\right)\left(-m^{2}-m-1\right)} times \frac{-1}{-1}.

$$\frac{-\left(1-6m\right)}{\left(m-1\right)\left(m^{2}+m+1\right)}-\frac{5}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

Since \frac{-\left(1-6m\right)}{\left(m-1\right)\left(m^{2}+m+1\right)} and \frac{5}{\left(m-1\right)\left(m^{2}+m+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\left(1-6m\right)-5}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

Do the multiplications in -\left(1-6m\right)-5.

$$\frac{-1+6m-5}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

Combine like terms in -1+6m-5.

$$\frac{-6+6m}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

Factor the expressions that are not already factored in \frac{-6+6m}{\left(m-1\right)\left(m^{2}+m+1\right)}.

$$\frac{6\left(m-1\right)}{\left(m-1\right)\left(m^{2}+m+1\right)}$$

Cancel out m-1 in both numerator and denominator.

$$\frac{6}{m^{2}+m+1}$$