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

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

Evaluate

$$\frac{45a^{3}}{14x^{2}}-\frac{49\times \left(\frac{x}{a}\right)^{4}}{18}$$

Short Solution Steps

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^{3}}{14x^{2}} times \frac{9a^{4}}{9a^{4}}. Multiply \frac{49x^{4}}{18a^{4}} times \frac{7x^{2}}{7x^{2}}.

$$\frac{45a^{3}\times 9a^{4}}{126x^{2}a^{4}}-\frac{49x^{4}\times 7x^{2}}{126x^{2}a^{4}}$$

Since \frac{45a^{3}\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.

$$\frac{45a^{3}\times 9a^{4}-49x^{4}\times 7x^{2}}{126x^{2}a^{4}}$$

Do the multiplications in 45a^{3}\times 9a^{4}-49x^{4}\times 7x^{2}.

$$\frac{405a^{7}-343x^{6}}{126x^{2}a^{4}}$$

Factor

$$\frac{405a^{7}-343x^{6}}{126x^{2}a^{4}}$$