Solve -3/4x^2+6/6x^2-3/4x^2

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

Evaluate

$$-\frac{1}{2x^{2}}$$

Short Solution Steps

Combine -\frac{3}{4x^{2}} and -\frac{3}{4x^{2}} to get 2\left(-\frac{3}{4x^{2}}\right).

$$2\left(-\frac{3}{4x^{2}}\right)+\frac{6}{6x^{2}}$$

Express 2\left(-\frac{3}{4x^{2}}\right) as a single fraction.

$$\frac{-2\times 3}{4x^{2}}+\frac{6}{6x^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-3}{2x^{2}}+\frac{6}{6x^{2}}$$

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

$$\frac{3\left(-1\right)\times 3}{6x^{2}}+\frac{6}{6x^{2}}$$

Since \frac{3\left(-1\right)\times 3}{6x^{2}} and \frac{6}{6x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{3\left(-1\right)\times 3+6}{6x^{2}}$$

Do the multiplications in 3\left(-1\right)\times 3+6.

$$\frac{-9+6}{6x^{2}}$$

Do the calculations in -9+6.

$$\frac{-3}{6x^{2}}$$

Differentiate w.r.t. x

$$\frac{1}{x^{3}}$$