Solve 3/2a^2-8a-5a/2

$$\frac { 3 } { 2 a ^ { 2 } - 8 a } - \frac { 5 a } { 2 }$$

Evaluate

$$\frac{3+20a^{2}-5a^{3}}{2a\left(a-4\right)}$$

Short Solution Steps

Factor 2a^{2}-8a.

$$\frac{3}{2a\left(a-4\right)}-\frac{5a}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a\left(a-4\right) and 2 is 2a\left(a-4\right). Multiply \frac{5a}{2} times \frac{a\left(a-4\right)}{a\left(a-4\right)}.

$$\frac{3}{2a\left(a-4\right)}-\frac{5aa\left(a-4\right)}{2a\left(a-4\right)}$$

Since \frac{3}{2a\left(a-4\right)} and \frac{5aa\left(a-4\right)}{2a\left(a-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-5aa\left(a-4\right)}{2a\left(a-4\right)}$$

Do the multiplications in 3-5aa\left(a-4\right).

$$\frac{3-5a^{3}+20a^{2}}{2a\left(a-4\right)}$$

Expand 2a\left(a-4\right).

$$\frac{3-5a^{3}+20a^{2}}{2a^{2}-8a}$$

Factor

$$\frac{3+20a^{2}-5a^{3}}{2a\left(a-4\right)}$$