Solve 2/3x^2-1/4x^7+7/6x^3

$$\frac { 2 } { 3 x ^ { 2 } } - \frac { 1 } { 4 x ^ { 7 } } + \frac { 7 } { 6 x ^ { 3 } }$$

Evaluate

$$\frac{2}{3x^{2}}+\frac{7}{6x^{3}}-\frac{1}{4x^{7}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x^{2} and 4x^{7} is 12x^{7}. Multiply \frac{2}{3x^{2}} times \frac{4x^{5}}{4x^{5}}. Multiply \frac{1}{4x^{7}} times \frac{3}{3}.

$$\frac{2\times 4x^{5}}{12x^{7}}-\frac{3}{12x^{7}}+\frac{7}{6x^{3}}$$

Since \frac{2\times 4x^{5}}{12x^{7}} and \frac{3}{12x^{7}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 4x^{5}-3}{12x^{7}}+\frac{7}{6x^{3}}$$

Do the multiplications in 2\times 4x^{5}-3.

$$\frac{8x^{5}-3}{12x^{7}}+\frac{7}{6x^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12x^{7} and 6x^{3} is 12x^{7}. Multiply \frac{7}{6x^{3}} times \frac{2x^{4}}{2x^{4}}.

$$\frac{8x^{5}-3}{12x^{7}}+\frac{7\times 2x^{4}}{12x^{7}}$$

Since \frac{8x^{5}-3}{12x^{7}} and \frac{7\times 2x^{4}}{12x^{7}} have the same denominator, add them by adding their numerators.

$$\frac{8x^{5}-3+7\times 2x^{4}}{12x^{7}}$$

Do the multiplications in 8x^{5}-3+7\times 2x^{4}.

$$\frac{8x^{5}-3+14x^{4}}{12x^{7}}$$

Factor

$$\frac{8x^{5}+14x^{4}-3}{12x^{2}x^{5}}$$