Solve 5y^2-19y-4/y+5*y^2+10y+25/5y^2+26y+5

$$\frac { 5 y ^ { 2 } - 19 y - 4 } { y + 5 } \cdot \frac { y ^ { 2 } + 10 y + 25 } { 5 y ^ { 2 } + 26 y + 5 }$$

Evaluate

$$y-4$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}+10y+25}{5y^{2}+26y+5}.

$$\frac{5y^{2}-19y-4}{y+5}\times \frac{\left(y+5\right)^{2}}{\left(y+5\right)\left(5y+1\right)}$$

Cancel out y+5 in both numerator and denominator.

$$\frac{5y^{2}-19y-4}{y+5}\times \frac{y+5}{5y+1}$$

Multiply \frac{5y^{2}-19y-4}{y+5} times \frac{y+5}{5y+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(5y^{2}-19y-4\right)\left(y+5\right)}{\left(y+5\right)\left(5y+1\right)}$$

Cancel out y+5 in both numerator and denominator.

$$\frac{5y^{2}-19y-4}{5y+1}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-4\right)\left(5y+1\right)}{5y+1}$$

Cancel out 5y+1 in both numerator and denominator.

$$y-4$$

Expand

$$y-4$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}+10y+25}{5y^{2}+26y+5}.

$$\frac{5y^{2}-19y-4}{y+5}\times \frac{\left(y+5\right)^{2}}{\left(y+5\right)\left(5y+1\right)}$$

Cancel out y+5 in both numerator and denominator.

$$\frac{5y^{2}-19y-4}{y+5}\times \frac{y+5}{5y+1}$$

Multiply \frac{5y^{2}-19y-4}{y+5} times \frac{y+5}{5y+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(5y^{2}-19y-4\right)\left(y+5\right)}{\left(y+5\right)\left(5y+1\right)}$$

Cancel out y+5 in both numerator and denominator.

$$\frac{5y^{2}-19y-4}{5y+1}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-4\right)\left(5y+1\right)}{5y+1}$$

Cancel out 5y+1 in both numerator and denominator.

$$y-4$$