Solve -3/5-c^2-15/2c

$$- \frac { 3 } { 5 } - \frac { c ^ { 2 } - 15 } { 2 c }$$

Evaluate

$$-\frac{c}{2}-\frac{3}{5}+\frac{15}{2c}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2c is 10c. Multiply -\frac{3}{5} times \frac{2c}{2c}. Multiply \frac{c^{2}-15}{2c} times \frac{5}{5}.

$$-\frac{3\times 2c}{10c}-\frac{5\left(c^{2}-15\right)}{10c}$$

Since -\frac{3\times 2c}{10c} and \frac{5\left(c^{2}-15\right)}{10c} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3\times 2c-5\left(c^{2}-15\right)}{10c}$$

Do the multiplications in -3\times 2c-5\left(c^{2}-15\right).

$$\frac{-6c-5c^{2}+75}{10c}$$

Factor the expressions that are not already factored in \frac{-6c-5c^{2}+75}{10c}.

$$\frac{-5\left(c-\left(-\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)\left(c-\left(\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)}{10c}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-\left(c-\left(-\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)\left(c-\left(\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)}{2c}$$

Cancel out -1 in both numerator and denominator.

$$\frac{\left(c-\left(-\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)\left(c-\left(\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)}{-2c}$$

To find the opposite of -\frac{8}{5}\sqrt{6}-\frac{3}{5}, find the opposite of each term.

$$\frac{\left(c+\frac{8}{5}\sqrt{6}+\frac{3}{5}\right)\left(c-\left(\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)}{-2c}$$

To find the opposite of \frac{8}{5}\sqrt{6}-\frac{3}{5}, find the opposite of each term.

$$\frac{\left(c+\frac{8}{5}\sqrt{6}+\frac{3}{5}\right)\left(c-\frac{8}{5}\sqrt{6}+\frac{3}{5}\right)}{-2c}$$

Use the distributive property to multiply c+\frac{8}{5}\sqrt{6}+\frac{3}{5} by c-\frac{8}{5}\sqrt{6}+\frac{3}{5} and combine like terms.

$$\frac{c^{2}+\frac{6}{5}c-\frac{64}{25}\left(\sqrt{6}\right)^{2}+\frac{9}{25}}{-2c}$$

The square of \sqrt{6} is 6.

$$\frac{c^{2}+\frac{6}{5}c-\frac{64}{25}\times 6+\frac{9}{25}}{-2c}$$

Multiply -\frac{64}{25} and 6 to get -\frac{384}{25}.

$$\frac{c^{2}+\frac{6}{5}c-\frac{384}{25}+\frac{9}{25}}{-2c}$$

Add -\frac{384}{25} and \frac{9}{25} to get -15.

$$\frac{c^{2}+\frac{6}{5}c-15}{-2c}$$

Expand

$$-\frac{c}{2}-\frac{3}{5}+\frac{15}{2c}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2c is 10c. Multiply -\frac{3}{5} times \frac{2c}{2c}. Multiply \frac{c^{2}-15}{2c} times \frac{5}{5}.

$$-\frac{3\times 2c}{10c}-\frac{5\left(c^{2}-15\right)}{10c}$$

Since -\frac{3\times 2c}{10c} and \frac{5\left(c^{2}-15\right)}{10c} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3\times 2c-5\left(c^{2}-15\right)}{10c}$$

Do the multiplications in -3\times 2c-5\left(c^{2}-15\right).

$$\frac{-6c-5c^{2}+75}{10c}$$

Factor the expressions that are not already factored in \frac{-6c-5c^{2}+75}{10c}.

$$\frac{-5\left(c-\left(-\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)\left(c-\left(\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)}{10c}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-\left(c-\left(-\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)\left(c-\left(\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)}{2c}$$

Cancel out -1 in both numerator and denominator.

$$\frac{\left(c-\left(-\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)\left(c-\left(\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)}{-2c}$$

To find the opposite of -\frac{8}{5}\sqrt{6}-\frac{3}{5}, find the opposite of each term.

$$\frac{\left(c+\frac{8}{5}\sqrt{6}+\frac{3}{5}\right)\left(c-\left(\frac{8}{5}\sqrt{6}-\frac{3}{5}\right)\right)}{-2c}$$

To find the opposite of \frac{8}{5}\sqrt{6}-\frac{3}{5}, find the opposite of each term.

$$\frac{\left(c+\frac{8}{5}\sqrt{6}+\frac{3}{5}\right)\left(c-\frac{8}{5}\sqrt{6}+\frac{3}{5}\right)}{-2c}$$

Use the distributive property to multiply c+\frac{8}{5}\sqrt{6}+\frac{3}{5} by c-\frac{8}{5}\sqrt{6}+\frac{3}{5} and combine like terms.

$$\frac{c^{2}+\frac{6}{5}c-\frac{64}{25}\left(\sqrt{6}\right)^{2}+\frac{9}{25}}{-2c}$$

The square of \sqrt{6} is 6.

$$\frac{c^{2}+\frac{6}{5}c-\frac{64}{25}\times 6+\frac{9}{25}}{-2c}$$

Multiply -\frac{64}{25} and 6 to get -\frac{384}{25}.

$$\frac{c^{2}+\frac{6}{5}c-\frac{384}{25}+\frac{9}{25}}{-2c}$$

Add -\frac{384}{25} and \frac{9}{25} to get -15.

$$\frac{c^{2}+\frac{6}{5}c-15}{-2c}$$