Solve 5s/(16s^2-25t^2)-s/(4s-5t)

$$\frac { 5 s } { ( 16 s ^ { 2 } - 25 t ^ { 2 } ) } - \frac { s } { ( 4 s - 5 t ) }$$

Evaluate

$$\frac{s\left(5-5t-4s\right)}{16s^{2}-25t^{2}}$$

Short Solution Steps

Factor 16s^{2}-25t^{2}.

$$\frac{5s}{\left(4s-5t\right)\left(4s+5t\right)}-\frac{s}{4s-5t}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(4s-5t\right)\left(4s+5t\right) and 4s-5t is \left(4s-5t\right)\left(4s+5t\right). Multiply \frac{s}{4s-5t} times \frac{4s+5t}{4s+5t}.

$$\frac{5s}{\left(4s-5t\right)\left(4s+5t\right)}-\frac{s\left(4s+5t\right)}{\left(4s-5t\right)\left(4s+5t\right)}$$

Since \frac{5s}{\left(4s-5t\right)\left(4s+5t\right)} and \frac{s\left(4s+5t\right)}{\left(4s-5t\right)\left(4s+5t\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5s-s\left(4s+5t\right)}{\left(4s-5t\right)\left(4s+5t\right)}$$

Do the multiplications in 5s-s\left(4s+5t\right).

$$\frac{5s-4s^{2}-5st}{\left(4s-5t\right)\left(4s+5t\right)}$$

Expand \left(4s-5t\right)\left(4s+5t\right).

$$\frac{5s-4s^{2}-5st}{16s^{2}-25t^{2}}$$

Factor

$$\frac{s\left(5-5t-4s\right)}{16s^{2}-25t^{2}}$$