Solve e*e^2/25-f^2/36

$$e \cdot \frac { e ^ { 2 } } { 25 } - \frac { f ^ { 2 } } { 36 }$$

Evaluate

$$-\frac{f^{2}}{36}+\frac{e^{3}}{25}$$

Short Solution Steps

Express e\times \frac{e^{2}}{25} as a single fraction.

$$\frac{ee^{2}}{25}-\frac{f^{2}}{36}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 36 is 900. Multiply \frac{ee^{2}}{25} times \frac{36}{36}. Multiply \frac{f^{2}}{36} times \frac{25}{25}.

$$\frac{36ee^{2}}{900}-\frac{25f^{2}}{900}$$

Since \frac{36ee^{2}}{900} and \frac{25f^{2}}{900} have the same denominator, subtract them by subtracting their numerators.

$$\frac{36ee^{2}-25f^{2}}{900}$$

Do the multiplications in 36ee^{2}-25f^{2}.

$$\frac{36e^{3}-25f^{2}}{900}$$

Factor

$$\frac{36e^{3}-25f^{2}}{900}$$

Solution Steps

Factor out \frac{1}{900}. Polynomial 36e^{3}-25f^{2} is not factored since it does not have any rational roots.

$$\frac{36ee^{2}-25f^{2}}{900}$$