Solve 7s/(4s^2-16t^2)-s/(2s-4t)

$$\frac { 7 s } { ( 4 s ^ { 2 } - 16 t ^ { 2 } ) } - \frac { s } { ( 2 s - 4 t ) }$$

Evaluate

$$\frac{s\left(7-4t-2s\right)}{4\left(s^{2}-4t^{2}\right)}$$

Short Solution Steps

Factor 4s^{2}-16t^{2}. Factor 2s-4t.

$$\frac{7s}{4\left(s-2t\right)\left(s+2t\right)}-\frac{s}{2\left(s-2t\right)}$$

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

$$\frac{7s}{4\left(s-2t\right)\left(s+2t\right)}-\frac{s\times 2\left(s+2t\right)}{4\left(s-2t\right)\left(s+2t\right)}$$

Since \frac{7s}{4\left(s-2t\right)\left(s+2t\right)} and \frac{s\times 2\left(s+2t\right)}{4\left(s-2t\right)\left(s+2t\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7s-s\times 2\left(s+2t\right)}{4\left(s-2t\right)\left(s+2t\right)}$$

Do the multiplications in 7s-s\times 2\left(s+2t\right).

$$\frac{7s-2s^{2}-4st}{4\left(s-2t\right)\left(s+2t\right)}$$

Expand 4\left(s-2t\right)\left(s+2t\right).

$$\frac{7s-2s^{2}-4st}{4s^{2}-16t^{2}}$$

Factor

$$\frac{s\left(7-4t-2s\right)}{4\left(s^{2}-4t^{2}\right)}$$