Solve y^2-6y-7/y^2-25divy-7

$$\frac{ { y }^{ 2 } -6y-7 }{ { y }^{ 2 } -25 } \div y-7$$

Evaluate

$$\frac{-7y^{3}+y^{2}+169y-7}{y\left(y^{2}-25\right)}$$

Short Solution Steps

Express \frac{\frac{y^{2}-6y-7}{y^{2}-25}}{y} as a single fraction.

$$\frac{y^{2}-6y-7}{\left(y^{2}-25\right)y}-7$$

Factor \left(y^{2}-25\right)y.

$$\frac{y^{2}-6y-7}{y\left(y-5\right)\left(y+5\right)}-7$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{y\left(y-5\right)\left(y+5\right)}{y\left(y-5\right)\left(y+5\right)}.

$$\frac{y^{2}-6y-7}{y\left(y-5\right)\left(y+5\right)}-\frac{7y\left(y-5\right)\left(y+5\right)}{y\left(y-5\right)\left(y+5\right)}$$

Since \frac{y^{2}-6y-7}{y\left(y-5\right)\left(y+5\right)} and \frac{7y\left(y-5\right)\left(y+5\right)}{y\left(y-5\right)\left(y+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y^{2}-6y-7-7y\left(y-5\right)\left(y+5\right)}{y\left(y-5\right)\left(y+5\right)}$$

Do the multiplications in y^{2}-6y-7-7y\left(y-5\right)\left(y+5\right).

$$\frac{y^{2}-6y-7-7y^{3}-35y^{2}+35y^{2}+175y}{y\left(y-5\right)\left(y+5\right)}$$

Combine like terms in y^{2}-6y-7-7y^{3}-35y^{2}+35y^{2}+175y.

$$\frac{y^{2}+169y-7-7y^{3}}{y\left(y-5\right)\left(y+5\right)}$$

Expand y\left(y-5\right)\left(y+5\right).

$$\frac{y^{2}+169y-7-7y^{3}}{y^{3}-25y}$$

Expand

$$\frac{-7y^{3}+y^{2}+169y-7}{y\left(y^{2}-25\right)}$$

Short Solution Steps

Express \frac{\frac{y^{2}-6y-7}{y^{2}-25}}{y} as a single fraction.

$$\frac{y^{2}-6y-7}{\left(y^{2}-25\right)y}-7$$

Factor \left(y^{2}-25\right)y.

$$\frac{y^{2}-6y-7}{y\left(y-5\right)\left(y+5\right)}-7$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{y\left(y-5\right)\left(y+5\right)}{y\left(y-5\right)\left(y+5\right)}.

$$\frac{y^{2}-6y-7}{y\left(y-5\right)\left(y+5\right)}-\frac{7y\left(y-5\right)\left(y+5\right)}{y\left(y-5\right)\left(y+5\right)}$$

Since \frac{y^{2}-6y-7}{y\left(y-5\right)\left(y+5\right)} and \frac{7y\left(y-5\right)\left(y+5\right)}{y\left(y-5\right)\left(y+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y^{2}-6y-7-7y\left(y-5\right)\left(y+5\right)}{y\left(y-5\right)\left(y+5\right)}$$

Do the multiplications in y^{2}-6y-7-7y\left(y-5\right)\left(y+5\right).

$$\frac{y^{2}-6y-7-7y^{3}-35y^{2}+35y^{2}+175y}{y\left(y-5\right)\left(y+5\right)}$$

Combine like terms in y^{2}-6y-7-7y^{3}-35y^{2}+35y^{2}+175y.

$$\frac{y^{2}+169y-7-7y^{3}}{y\left(y-5\right)\left(y+5\right)}$$

Expand y\left(y-5\right)\left(y+5\right).

$$\frac{y^{2}+169y-7-7y^{3}}{y^{3}-25y}$$