Solve 50*50(y+75)/y+25/50+frac{50(y+75){y+25}}+y

$$\frac { 50 \cdot \frac { 50 ( y + 75 ) } { y + 25 } } { 50 + \frac { 50 ( y + 75 ) } { y + 25 } } + y$$

Evaluate

$$\frac{y^{2}+75y+1875}{y+50}$$

Short Solution Steps

Express 50\times \frac{50\left(y+75\right)}{y+25} as a single fraction.

$$\frac{\frac{50\times 50\left(y+75\right)}{y+25}}{50+\frac{50\left(y+75\right)}{y+25}}+y$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 50 times \frac{y+25}{y+25}.

$$\frac{\frac{50\times 50\left(y+75\right)}{y+25}}{\frac{50\left(y+25\right)}{y+25}+\frac{50\left(y+75\right)}{y+25}}+y$$

Since \frac{50\left(y+25\right)}{y+25} and \frac{50\left(y+75\right)}{y+25} have the same denominator, add them by adding their numerators.

$$\frac{\frac{50\times 50\left(y+75\right)}{y+25}}{\frac{50\left(y+25\right)+50\left(y+75\right)}{y+25}}+y$$

Do the multiplications in 50\left(y+25\right)+50\left(y+75\right).

$$\frac{\frac{50\times 50\left(y+75\right)}{y+25}}{\frac{50y+1250+50y+3750}{y+25}}+y$$

Combine like terms in 50y+1250+50y+3750.

$$\frac{\frac{50\times 50\left(y+75\right)}{y+25}}{\frac{100y+5000}{y+25}}+y$$

Divide \frac{50\times 50\left(y+75\right)}{y+25} by \frac{100y+5000}{y+25} by multiplying \frac{50\times 50\left(y+75\right)}{y+25} by the reciprocal of \frac{100y+5000}{y+25}.

$$\frac{50\times 50\left(y+75\right)\left(y+25\right)}{\left(y+25\right)\left(100y+5000\right)}+y$$

Cancel out y+25 in both numerator and denominator.

$$\frac{50\times 50\left(y+75\right)}{100y+5000}+y$$

Multiply 50 and 50 to get 2500.

$$\frac{2500\left(y+75\right)}{100y+5000}+y$$

Factor the expressions that are not already factored in \frac{2500\left(y+75\right)}{100y+5000}.

$$\frac{2500\left(y+75\right)}{100\left(y+50\right)}+y$$

Cancel out 100 in both numerator and denominator.

$$\frac{25\left(y+75\right)}{y+50}+y$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{y+50}{y+50}.

$$\frac{25\left(y+75\right)}{y+50}+\frac{y\left(y+50\right)}{y+50}$$

Since \frac{25\left(y+75\right)}{y+50} and \frac{y\left(y+50\right)}{y+50} have the same denominator, add them by adding their numerators.

$$\frac{25\left(y+75\right)+y\left(y+50\right)}{y+50}$$

Do the multiplications in 25\left(y+75\right)+y\left(y+50\right).

$$\frac{25y+1875+y^{2}+50y}{y+50}$$

Combine like terms in 25y+1875+y^{2}+50y.

$$\frac{75y+1875+y^{2}}{y+50}$$

Expand

$$\frac{y^{2}+75y+1875}{y+50}$$

Short Solution Steps

Express 50\times \frac{50\left(y+75\right)}{y+25} as a single fraction.

$$\frac{\frac{50\times 50\left(y+75\right)}{y+25}}{50+\frac{50\left(y+75\right)}{y+25}}+y$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 50 times \frac{y+25}{y+25}.

$$\frac{\frac{50\times 50\left(y+75\right)}{y+25}}{\frac{50\left(y+25\right)}{y+25}+\frac{50\left(y+75\right)}{y+25}}+y$$

Since \frac{50\left(y+25\right)}{y+25} and \frac{50\left(y+75\right)}{y+25} have the same denominator, add them by adding their numerators.

$$\frac{\frac{50\times 50\left(y+75\right)}{y+25}}{\frac{50\left(y+25\right)+50\left(y+75\right)}{y+25}}+y$$

Do the multiplications in 50\left(y+25\right)+50\left(y+75\right).

$$\frac{\frac{50\times 50\left(y+75\right)}{y+25}}{\frac{50y+1250+50y+3750}{y+25}}+y$$

Combine like terms in 50y+1250+50y+3750.

$$\frac{\frac{50\times 50\left(y+75\right)}{y+25}}{\frac{100y+5000}{y+25}}+y$$

Divide \frac{50\times 50\left(y+75\right)}{y+25} by \frac{100y+5000}{y+25} by multiplying \frac{50\times 50\left(y+75\right)}{y+25} by the reciprocal of \frac{100y+5000}{y+25}.

$$\frac{50\times 50\left(y+75\right)\left(y+25\right)}{\left(y+25\right)\left(100y+5000\right)}+y$$

Cancel out y+25 in both numerator and denominator.

$$\frac{50\times 50\left(y+75\right)}{100y+5000}+y$$

Multiply 50 and 50 to get 2500.

$$\frac{2500\left(y+75\right)}{100y+5000}+y$$

Factor the expressions that are not already factored in \frac{2500\left(y+75\right)}{100y+5000}.

$$\frac{2500\left(y+75\right)}{100\left(y+50\right)}+y$$

Cancel out 100 in both numerator and denominator.

$$\frac{25\left(y+75\right)}{y+50}+y$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{y+50}{y+50}.

$$\frac{25\left(y+75\right)}{y+50}+\frac{y\left(y+50\right)}{y+50}$$

Since \frac{25\left(y+75\right)}{y+50} and \frac{y\left(y+50\right)}{y+50} have the same denominator, add them by adding their numerators.

$$\frac{25\left(y+75\right)+y\left(y+50\right)}{y+50}$$

Do the multiplications in 25\left(y+75\right)+y\left(y+50\right).

$$\frac{25y+1875+y^{2}+50y}{y+50}$$

Combine like terms in 25y+1875+y^{2}+50y.

$$\frac{75y+1875+y^{2}}{y+50}$$