Solve 45a^3/14ax^2-49x^4/18a^4=

$$\frac { 45 a ^ { 3 } } { 14 a x ^ { 2 } } - \frac { 49 x ^ { 4 } } { 18 a ^ { 4 } } =$$

Evaluate

$$\frac{45\times \left(\frac{a}{x}\right)^{2}}{14}-\frac{49\times \left(\frac{x}{a}\right)^{4}}{18}$$

Short Solution Steps

Cancel out a in both numerator and denominator.

$$\frac{45a^{2}}{14x^{2}}-\frac{49x^{4}}{18a^{4}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 14x^{2} and 18a^{4} is 126x^{2}a^{4}. Multiply \frac{45a^{2}}{14x^{2}} times \frac{9a^{4}}{9a^{4}}. Multiply \frac{49x^{4}}{18a^{4}} times \frac{7x^{2}}{7x^{2}}.

$$\frac{45a^{2}\times 9a^{4}}{126x^{2}a^{4}}-\frac{49x^{4}\times 7x^{2}}{126x^{2}a^{4}}$$

Since \frac{45a^{2}\times 9a^{4}}{126x^{2}a^{4}} and \frac{49x^{4}\times 7x^{2}}{126x^{2}a^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45a^{2}\times 9a^{4}-49x^{4}\times 7x^{2}}{126x^{2}a^{4}}$$

Do the multiplications in 45a^{2}\times 9a^{4}-49x^{4}\times 7x^{2}.

$$\frac{405a^{6}-343x^{6}}{126x^{2}a^{4}}$$

Factor

$$\frac{405a^{6}-343x^{6}}{126x^{2}a^{4}}$$