Solve x^5/49-4x^10/121

$$\frac{ { x }^{ 5 } }{ 49 } - \frac{ 4 { x }^{ 10 } }{ 121 }$$

Evaluate

$$-\frac{4x^{10}}{121}+\frac{x^{5}}{49}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 49 and 121 is 5929. Multiply \frac{x^{5}}{49} times \frac{121}{121}. Multiply \frac{4x^{10}}{121} times \frac{49}{49}.

$$\frac{121x^{5}}{5929}-\frac{49\times 4x^{10}}{5929}$$

Since \frac{121x^{5}}{5929} and \frac{49\times 4x^{10}}{5929} have the same denominator, subtract them by subtracting their numerators.

$$\frac{121x^{5}-49\times 4x^{10}}{5929}$$

Do the multiplications in 121x^{5}-49\times 4x^{10}.

$$\frac{121x^{5}-196x^{10}}{5929}$$

Factor

$$\frac{x^{5}\left(121-196x^{5}\right)}{5929}$$

Solution Steps

Factor out \frac{1}{5929}.

$$\frac{121x^{5}-196x^{10}}{5929}$$

Consider 121x^{5}-196x^{10}. Factor out x^{5}.

$$x^{5}\left(121-196x^{5}\right)$$

Rewrite the complete factored expression. Polynomial 121-196x^{5} is not factored since it does not have any rational roots.

$$\frac{x^{5}\left(121-196x^{5}\right)}{5929}$$