Solve 3a^2-20a+24-64/a+64/a^2

$$3 { a }^{ 2 } -20a+24- \frac{ 64 }{ a } + \frac{ 64 }{ { a }^{ 2 } }$$

Evaluate

$$3a^{2}-20a+24-\frac{64}{a}+\frac{64}{a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3a^{2}-20a+24 times \frac{a}{a}.

$$\frac{\left(3a^{2}-20a+24\right)a}{a}-\frac{64}{a}+\frac{64}{a^{2}}$$

Since \frac{\left(3a^{2}-20a+24\right)a}{a} and \frac{64}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(3a^{2}-20a+24\right)a-64}{a}+\frac{64}{a^{2}}$$

Do the multiplications in \left(3a^{2}-20a+24\right)a-64.

$$\frac{3a^{3}-20a^{2}+24a-64}{a}+\frac{64}{a^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and a^{2} is a^{2}. Multiply \frac{3a^{3}-20a^{2}+24a-64}{a} times \frac{a}{a}.

$$\frac{\left(3a^{3}-20a^{2}+24a-64\right)a}{a^{2}}+\frac{64}{a^{2}}$$

Since \frac{\left(3a^{3}-20a^{2}+24a-64\right)a}{a^{2}} and \frac{64}{a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(3a^{3}-20a^{2}+24a-64\right)a+64}{a^{2}}$$

Do the multiplications in \left(3a^{3}-20a^{2}+24a-64\right)a+64.

$$\frac{3a^{4}-20a^{3}+24a^{2}-64a+64}{a^{2}}$$

Factor

$$\frac{3a^{4}-20a^{3}+24a^{2}-64a+64}{a^{2}}$$