Solve a^2+c^2-2c^2-2a^2/3/2ac

$$\frac { a ^ { 2 } + c ^ { 2 } - \frac { 2 c ^ { 2 } - 2 a ^ { 2 } } { 3 } } { 2 a c }$$

Evaluate

$$\frac{5a^{2}+c^{2}}{6ac}$$

Short Solution Steps

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

$$\frac{\frac{3\left(a^{2}+c^{2}\right)}{3}-\frac{2c^{2}-2a^{2}}{3}}{2ac}$$

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

$$\frac{\frac{3\left(a^{2}+c^{2}\right)-\left(2c^{2}-2a^{2}\right)}{3}}{2ac}$$

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

$$\frac{\frac{3a^{2}+3c^{2}-2c^{2}+2a^{2}}{3}}{2ac}$$

Combine like terms in 3a^{2}+3c^{2}-2c^{2}+2a^{2}.

$$\frac{\frac{5a^{2}+c^{2}}{3}}{2ac}$$

Express \frac{\frac{5a^{2}+c^{2}}{3}}{2ac} as a single fraction.

$$\frac{5a^{2}+c^{2}}{3\times 2ac}$$

Multiply 3 and 2 to get 6.

$$\frac{5a^{2}+c^{2}}{6ac}$$

Expand

$$\frac{5a^{2}+c^{2}}{6ac}$$

Short Solution Steps

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

$$\frac{\frac{3\left(a^{2}+c^{2}\right)}{3}-\frac{2c^{2}-2a^{2}}{3}}{2ac}$$

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

$$\frac{\frac{3\left(a^{2}+c^{2}\right)-\left(2c^{2}-2a^{2}\right)}{3}}{2ac}$$

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

$$\frac{\frac{3a^{2}+3c^{2}-2c^{2}+2a^{2}}{3}}{2ac}$$

Combine like terms in 3a^{2}+3c^{2}-2c^{2}+2a^{2}.

$$\frac{\frac{5a^{2}+c^{2}}{3}}{2ac}$$

Express \frac{\frac{5a^{2}+c^{2}}{3}}{2ac} as a single fraction.

$$\frac{5a^{2}+c^{2}}{3\times 2ac}$$

Multiply 3 and 2 to get 6.

$$\frac{5a^{2}+c^{2}}{6ac}$$