Solve 8/3t^2-15t-3/2t-10

$$\frac { 8 } { 3 t ^ { 2 } - 15 t } - \frac { 3 } { 2 t - 10 }$$

Evaluate

$$-\frac{9t-16}{6t\left(t-5\right)}$$

Short Solution Steps

Factor 3t^{2}-15t. Factor 2t-10.

$$\frac{8}{3t\left(t-5\right)}-\frac{3}{2\left(t-5\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3t\left(t-5\right) and 2\left(t-5\right) is 6t\left(t-5\right). Multiply \frac{8}{3t\left(t-5\right)} times \frac{2}{2}. Multiply \frac{3}{2\left(t-5\right)} times \frac{3t}{3t}.

$$\frac{8\times 2}{6t\left(t-5\right)}-\frac{3\times 3t}{6t\left(t-5\right)}$$

Since \frac{8\times 2}{6t\left(t-5\right)} and \frac{3\times 3t}{6t\left(t-5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8\times 2-3\times 3t}{6t\left(t-5\right)}$$

Do the multiplications in 8\times 2-3\times 3t.

$$\frac{16-9t}{6t\left(t-5\right)}$$

Expand 6t\left(t-5\right).

$$\frac{16-9t}{6t^{2}-30t}$$

Factor

$$-\frac{9t-16}{6t\left(t-5\right)}$$