Solve 16/m-3-4/m-4/frac{16{m^2}-m-4/m-3}

$$\frac { \frac { 16 } { m - 3 } - \frac { 4 } { m - 4 } } { \frac { 16 } { m ^ { 2 } } - \frac { m - 4 } { m - 3 } }$$

Evaluate

$$\frac{4\left(3m-13\right)m^{2}}{\left(m-4\right)\left(-m^{3}+4m^{2}+16m-48\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m-3 and m-4 is \left(m-4\right)\left(m-3\right). Multiply \frac{16}{m-3} times \frac{m-4}{m-4}. Multiply \frac{4}{m-4} times \frac{m-3}{m-3}.

$$\frac{\frac{16\left(m-4\right)}{\left(m-4\right)\left(m-3\right)}-\frac{4\left(m-3\right)}{\left(m-4\right)\left(m-3\right)}}{\frac{16}{m^{2}}-\frac{m-4}{m-3}}$$

Since \frac{16\left(m-4\right)}{\left(m-4\right)\left(m-3\right)} and \frac{4\left(m-3\right)}{\left(m-4\right)\left(m-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16\left(m-4\right)-4\left(m-3\right)}{\left(m-4\right)\left(m-3\right)}}{\frac{16}{m^{2}}-\frac{m-4}{m-3}}$$

Do the multiplications in 16\left(m-4\right)-4\left(m-3\right).

$$\frac{\frac{16m-64-4m+12}{\left(m-4\right)\left(m-3\right)}}{\frac{16}{m^{2}}-\frac{m-4}{m-3}}$$

Combine like terms in 16m-64-4m+12.

$$\frac{\frac{12m-52}{\left(m-4\right)\left(m-3\right)}}{\frac{16}{m^{2}}-\frac{m-4}{m-3}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m^{2} and m-3 is \left(m-3\right)m^{2}. Multiply \frac{16}{m^{2}} times \frac{m-3}{m-3}. Multiply \frac{m-4}{m-3} times \frac{m^{2}}{m^{2}}.

$$\frac{\frac{12m-52}{\left(m-4\right)\left(m-3\right)}}{\frac{16\left(m-3\right)}{\left(m-3\right)m^{2}}-\frac{\left(m-4\right)m^{2}}{\left(m-3\right)m^{2}}}$$

Since \frac{16\left(m-3\right)}{\left(m-3\right)m^{2}} and \frac{\left(m-4\right)m^{2}}{\left(m-3\right)m^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{12m-52}{\left(m-4\right)\left(m-3\right)}}{\frac{16\left(m-3\right)-\left(m-4\right)m^{2}}{\left(m-3\right)m^{2}}}$$

Do the multiplications in 16\left(m-3\right)-\left(m-4\right)m^{2}.

$$\frac{\frac{12m-52}{\left(m-4\right)\left(m-3\right)}}{\frac{16m-48-m^{3}+4m^{2}}{\left(m-3\right)m^{2}}}$$

Divide \frac{12m-52}{\left(m-4\right)\left(m-3\right)} by \frac{16m-48-m^{3}+4m^{2}}{\left(m-3\right)m^{2}} by multiplying \frac{12m-52}{\left(m-4\right)\left(m-3\right)} by the reciprocal of \frac{16m-48-m^{3}+4m^{2}}{\left(m-3\right)m^{2}}.

$$\frac{\left(12m-52\right)\left(m-3\right)m^{2}}{\left(m-4\right)\left(m-3\right)\left(16m-48-m^{3}+4m^{2}\right)}$$

Cancel out m-3 in both numerator and denominator.

$$\frac{\left(12m-52\right)m^{2}}{\left(m-4\right)\left(-m^{3}+4m^{2}+16m-48\right)}$$

Use the distributive property to multiply 12m-52 by m^{2}.

$$\frac{12m^{3}-52m^{2}}{\left(m-4\right)\left(-m^{3}+4m^{2}+16m-48\right)}$$

Use the distributive property to multiply m-4 by -m^{3}+4m^{2}+16m-48 and combine like terms.

$$\frac{12m^{3}-52m^{2}}{-m^{4}+8m^{3}-112m+192}$$

Expand

$$\frac{4\left(3m^{3}-13m^{2}\right)}{\left(m-4\right)\left(-m^{3}+4m^{2}+16m-48\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m-3 and m-4 is \left(m-4\right)\left(m-3\right). Multiply \frac{16}{m-3} times \frac{m-4}{m-4}. Multiply \frac{4}{m-4} times \frac{m-3}{m-3}.

$$\frac{\frac{16\left(m-4\right)}{\left(m-4\right)\left(m-3\right)}-\frac{4\left(m-3\right)}{\left(m-4\right)\left(m-3\right)}}{\frac{16}{m^{2}}-\frac{m-4}{m-3}}$$

Since \frac{16\left(m-4\right)}{\left(m-4\right)\left(m-3\right)} and \frac{4\left(m-3\right)}{\left(m-4\right)\left(m-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16\left(m-4\right)-4\left(m-3\right)}{\left(m-4\right)\left(m-3\right)}}{\frac{16}{m^{2}}-\frac{m-4}{m-3}}$$

Do the multiplications in 16\left(m-4\right)-4\left(m-3\right).

$$\frac{\frac{16m-64-4m+12}{\left(m-4\right)\left(m-3\right)}}{\frac{16}{m^{2}}-\frac{m-4}{m-3}}$$

Combine like terms in 16m-64-4m+12.

$$\frac{\frac{12m-52}{\left(m-4\right)\left(m-3\right)}}{\frac{16}{m^{2}}-\frac{m-4}{m-3}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m^{2} and m-3 is \left(m-3\right)m^{2}. Multiply \frac{16}{m^{2}} times \frac{m-3}{m-3}. Multiply \frac{m-4}{m-3} times \frac{m^{2}}{m^{2}}.

$$\frac{\frac{12m-52}{\left(m-4\right)\left(m-3\right)}}{\frac{16\left(m-3\right)}{\left(m-3\right)m^{2}}-\frac{\left(m-4\right)m^{2}}{\left(m-3\right)m^{2}}}$$

Since \frac{16\left(m-3\right)}{\left(m-3\right)m^{2}} and \frac{\left(m-4\right)m^{2}}{\left(m-3\right)m^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{12m-52}{\left(m-4\right)\left(m-3\right)}}{\frac{16\left(m-3\right)-\left(m-4\right)m^{2}}{\left(m-3\right)m^{2}}}$$

Do the multiplications in 16\left(m-3\right)-\left(m-4\right)m^{2}.

$$\frac{\frac{12m-52}{\left(m-4\right)\left(m-3\right)}}{\frac{16m-48-m^{3}+4m^{2}}{\left(m-3\right)m^{2}}}$$

Divide \frac{12m-52}{\left(m-4\right)\left(m-3\right)} by \frac{16m-48-m^{3}+4m^{2}}{\left(m-3\right)m^{2}} by multiplying \frac{12m-52}{\left(m-4\right)\left(m-3\right)} by the reciprocal of \frac{16m-48-m^{3}+4m^{2}}{\left(m-3\right)m^{2}}.

$$\frac{\left(12m-52\right)\left(m-3\right)m^{2}}{\left(m-4\right)\left(m-3\right)\left(16m-48-m^{3}+4m^{2}\right)}$$

Cancel out m-3 in both numerator and denominator.

$$\frac{\left(12m-52\right)m^{2}}{\left(m-4\right)\left(-m^{3}+4m^{2}+16m-48\right)}$$

Use the distributive property to multiply 12m-52 by m^{2}.

$$\frac{12m^{3}-52m^{2}}{\left(m-4\right)\left(-m^{3}+4m^{2}+16m-48\right)}$$

Use the distributive property to multiply m-4 by -m^{3}+4m^{2}+16m-48 and combine like terms.

$$\frac{12m^{3}-52m^{2}}{-m^{4}+8m^{3}-112m+192}$$