Solve y^2/25+25-25y^2/9/9

$$\frac { y ^ { 2 } } { 25 } + \frac { 25 - \frac { 25 y ^ { 2 } } { 9 } } { 9 }$$

Evaluate

$$-\frac{544y^{2}}{2025}+\frac{25}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 25 times \frac{9}{9}.

$$\frac{y^{2}}{25}+\frac{\frac{25\times 9}{9}-\frac{25y^{2}}{9}}{9}$$

Since \frac{25\times 9}{9} and \frac{25y^{2}}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y^{2}}{25}+\frac{\frac{25\times 9-25y^{2}}{9}}{9}$$

Do the multiplications in 25\times 9-25y^{2}.

$$\frac{y^{2}}{25}+\frac{\frac{225-25y^{2}}{9}}{9}$$

Express \frac{\frac{225-25y^{2}}{9}}{9} as a single fraction.

$$\frac{y^{2}}{25}+\frac{225-25y^{2}}{9\times 9}$$

Multiply 9 and 9 to get 81.

$$\frac{y^{2}}{25}+\frac{225-25y^{2}}{81}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 81 is 2025. Multiply \frac{y^{2}}{25} times \frac{81}{81}. Multiply \frac{225-25y^{2}}{81} times \frac{25}{25}.

$$\frac{81y^{2}}{2025}+\frac{25\left(225-25y^{2}\right)}{2025}$$

Since \frac{81y^{2}}{2025} and \frac{25\left(225-25y^{2}\right)}{2025} have the same denominator, add them by adding their numerators.

$$\frac{81y^{2}+25\left(225-25y^{2}\right)}{2025}$$

Do the multiplications in 81y^{2}+25\left(225-25y^{2}\right).

$$\frac{81y^{2}+5625-625y^{2}}{2025}$$

Combine like terms in 81y^{2}+5625-625y^{2}.

$$\frac{-544y^{2}+5625}{2025}$$

Expand

$$-\frac{544y^{2}}{2025}+\frac{25}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 25 times \frac{9}{9}.

$$\frac{y^{2}}{25}+\frac{\frac{25\times 9}{9}-\frac{25y^{2}}{9}}{9}$$

Since \frac{25\times 9}{9} and \frac{25y^{2}}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y^{2}}{25}+\frac{\frac{25\times 9-25y^{2}}{9}}{9}$$

Do the multiplications in 25\times 9-25y^{2}.

$$\frac{y^{2}}{25}+\frac{\frac{225-25y^{2}}{9}}{9}$$

Express \frac{\frac{225-25y^{2}}{9}}{9} as a single fraction.

$$\frac{y^{2}}{25}+\frac{225-25y^{2}}{9\times 9}$$

Multiply 9 and 9 to get 81.

$$\frac{y^{2}}{25}+\frac{225-25y^{2}}{81}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25 and 81 is 2025. Multiply \frac{y^{2}}{25} times \frac{81}{81}. Multiply \frac{225-25y^{2}}{81} times \frac{25}{25}.

$$\frac{81y^{2}}{2025}+\frac{25\left(225-25y^{2}\right)}{2025}$$

Since \frac{81y^{2}}{2025} and \frac{25\left(225-25y^{2}\right)}{2025} have the same denominator, add them by adding their numerators.

$$\frac{81y^{2}+25\left(225-25y^{2}\right)}{2025}$$

Do the multiplications in 81y^{2}+25\left(225-25y^{2}\right).

$$\frac{81y^{2}+5625-625y^{2}}{2025}$$

Combine like terms in 81y^{2}+5625-625y^{2}.

$$\frac{-544y^{2}+5625}{2025}$$