Solve 36/a^2-25/6^2

$$\frac { 36 } { a ^ { 2 } } - \frac { 25 } { 6 ^ { 2 } }$$

Evaluate

$$-\frac{25}{36}+\frac{36}{a^{2}}$$

Short Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\frac{36}{a^{2}}-\frac{25}{36}$$

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

$$\frac{36\times 36}{36a^{2}}-\frac{25a^{2}}{36a^{2}}$$

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

$$\frac{36\times 36-25a^{2}}{36a^{2}}$$

Do the multiplications in 36\times 36-25a^{2}.

$$\frac{1296-25a^{2}}{36a^{2}}$$

Factor

$$-\frac{\frac{1}{36}\left(5a-36\right)\left(5a+36\right)}{a^{2}}$$