Solve x^2/3-y^2/2-z^2/4

$$\frac { x ^ { 2 } } { 3 } - \frac { y ^ { 2 } } { 2 } - \frac { z ^ { 2 } } { 4 }$$

Evaluate

$$\frac{x^{2}}{3}-\frac{y^{2}}{2}-\frac{z^{2}}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{x^{2}}{3} times \frac{2}{2}. Multiply \frac{y^{2}}{2} times \frac{3}{3}.

$$\frac{2x^{2}}{6}-\frac{3y^{2}}{6}-\frac{z^{2}}{4}$$

Since \frac{2x^{2}}{6} and \frac{3y^{2}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x^{2}-3y^{2}}{6}-\frac{z^{2}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 4 is 12. Multiply \frac{2x^{2}-3y^{2}}{6} times \frac{2}{2}. Multiply \frac{z^{2}}{4} times \frac{3}{3}.

$$\frac{2\left(2x^{2}-3y^{2}\right)}{12}-\frac{3z^{2}}{12}$$

Since \frac{2\left(2x^{2}-3y^{2}\right)}{12} and \frac{3z^{2}}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(2x^{2}-3y^{2}\right)-3z^{2}}{12}$$

Do the multiplications in 2\left(2x^{2}-3y^{2}\right)-3z^{2}.

$$\frac{4x^{2}-6y^{2}-3z^{2}}{12}$$

Factor

$$\frac{4x^{2}-6y^{2}-3z^{2}}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{4x^{2}-6y^{2}-3z^{2}}{12}$$