Solve 3/m^2-14m+49+2m/7-m

$$\frac { 3 } { m ^ { 2 } - 14 m + 49 } + \frac { 2 m } { 7 - m }$$

Evaluate

$$-\frac{2m^{2}-14m-3}{\left(7-m\right)^{2}}$$

Short Solution Steps

Factor m^{2}-14m+49.

$$\frac{3}{\left(m-7\right)^{2}}+\frac{2m}{7-m}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-7\right)^{2} and 7-m is \left(m-7\right)^{2}. Multiply \frac{2m}{7-m} times \frac{-\left(m-7\right)}{-\left(m-7\right)}.

$$\frac{3}{\left(m-7\right)^{2}}+\frac{2m\left(-1\right)\left(m-7\right)}{\left(m-7\right)^{2}}$$

Since \frac{3}{\left(m-7\right)^{2}} and \frac{2m\left(-1\right)\left(m-7\right)}{\left(m-7\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3+2m\left(-1\right)\left(m-7\right)}{\left(m-7\right)^{2}}$$

Do the multiplications in 3+2m\left(-1\right)\left(m-7\right).

$$\frac{3-2m^{2}+14m}{\left(m-7\right)^{2}}$$

Expand \left(m-7\right)^{2}.

$$\frac{3-2m^{2}+14m}{m^{2}-14m+49}$$

Differentiate w.r.t. m

$$\frac{2\left(52-7m\right)}{\left(7-m\right)\left(m-7\right)^{2}}$$