Solve 4s/(25s^2-9t^2)-s/(5s-3t)

$$\frac { 4 s } { ( 25 s ^ { 2 } - 9 t ^ { 2 } ) } - \frac { s } { ( 5 s - 3 t ) }$$

Evaluate

$$\frac{s\left(4-3t-5s\right)}{25s^{2}-9t^{2}}$$

Short Solution Steps

Factor 25s^{2}-9t^{2}.

$$\frac{4s}{\left(5s-3t\right)\left(5s+3t\right)}-\frac{s}{5s-3t}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(5s-3t\right)\left(5s+3t\right) and 5s-3t is \left(5s-3t\right)\left(5s+3t\right). Multiply \frac{s}{5s-3t} times \frac{5s+3t}{5s+3t}.

$$\frac{4s}{\left(5s-3t\right)\left(5s+3t\right)}-\frac{s\left(5s+3t\right)}{\left(5s-3t\right)\left(5s+3t\right)}$$

Since \frac{4s}{\left(5s-3t\right)\left(5s+3t\right)} and \frac{s\left(5s+3t\right)}{\left(5s-3t\right)\left(5s+3t\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4s-s\left(5s+3t\right)}{\left(5s-3t\right)\left(5s+3t\right)}$$

Do the multiplications in 4s-s\left(5s+3t\right).

$$\frac{4s-5s^{2}-3st}{\left(5s-3t\right)\left(5s+3t\right)}$$

Expand \left(5s-3t\right)\left(5s+3t\right).

$$\frac{4s-5s^{2}-3st}{25s^{2}-9t^{2}}$$

Factor

$$\frac{s\left(4-3t-5s\right)}{25s^{2}-9t^{2}}$$