Solve 9a^2+1/2a^2-2+2a-1/a

$$9 a ^ { 2 } + \frac { 1 } { 2 a ^ { 2 } } - 2 + 2 a - \frac { 1 } { a }$$

Evaluate

$$9a^{2}+2a-2-\frac{1}{a}+\frac{1}{2a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9a^{2}-2+2a times \frac{2a^{2}}{2a^{2}}.

$$\frac{\left(9a^{2}-2+2a\right)\times 2a^{2}}{2a^{2}}+\frac{1}{2a^{2}}-\frac{1}{a}$$

Since \frac{\left(9a^{2}-2+2a\right)\times 2a^{2}}{2a^{2}} and \frac{1}{2a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(9a^{2}-2+2a\right)\times 2a^{2}+1}{2a^{2}}-\frac{1}{a}$$

Do the multiplications in \left(9a^{2}-2+2a\right)\times 2a^{2}+1.

$$\frac{18a^{4}-4a^{2}+4a^{3}+1}{2a^{2}}-\frac{1}{a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a^{2} and a is 2a^{2}. Multiply \frac{1}{a} times \frac{2a}{2a}.

$$\frac{18a^{4}-4a^{2}+4a^{3}+1}{2a^{2}}-\frac{2a}{2a^{2}}$$

Since \frac{18a^{4}-4a^{2}+4a^{3}+1}{2a^{2}} and \frac{2a}{2a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18a^{4}-4a^{2}+4a^{3}+1-2a}{2a^{2}}$$

Factor

$$\frac{18a^{4}+4a^{3}-4a^{2}-2a+1}{2a^{2}}$$