Solve y+4/y-7+y^2+6y+8/y^2-5y-14-y^2-3y-28/y^2-14y+49

$$\frac { y + 4 } { y - 7 } + \frac { y ^ { 2 } + 6 y + 8 } { y ^ { 2 } - 5 y - 14 } - \frac { y ^ { 2 } - 3 y - 28 } { y ^ { 2 } - 14 y + 49 }$$

Evaluate

$$\frac{y+4}{y-7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}+6y+8}{y^{2}-5y-14}.

$$\frac{y+4}{y-7}+\frac{\left(y+2\right)\left(y+4\right)}{\left(y-7\right)\left(y+2\right)}-\frac{y^{2}-3y-28}{y^{2}-14y+49}$$

Cancel out y+2 in both numerator and denominator.

$$\frac{y+4}{y-7}+\frac{y+4}{y-7}-\frac{y^{2}-3y-28}{y^{2}-14y+49}$$

Combine \frac{y+4}{y-7} and \frac{y+4}{y-7} to get 2\times \frac{y+4}{y-7}.

$$2\times \frac{y+4}{y-7}-\frac{y^{2}-3y-28}{y^{2}-14y+49}$$

Factor the expressions that are not already factored in \frac{y^{2}-3y-28}{y^{2}-14y+49}.

$$2\times \frac{y+4}{y-7}-\frac{\left(y-7\right)\left(y+4\right)}{\left(y-7\right)^{2}}$$

Cancel out y-7 in both numerator and denominator.

$$2\times \frac{y+4}{y-7}-\frac{y+4}{y-7}$$

Express 2\times \frac{y+4}{y-7} as a single fraction.

$$\frac{2\left(y+4\right)}{y-7}-\frac{y+4}{y-7}$$

Since \frac{2\left(y+4\right)}{y-7} and \frac{y+4}{y-7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(y+4\right)-\left(y+4\right)}{y-7}$$

Do the multiplications in 2\left(y+4\right)-\left(y+4\right).

$$\frac{2y+8-y-4}{y-7}$$

Combine like terms in 2y+8-y-4.

$$\frac{y+4}{y-7}$$

Expand

$$\frac{y+4}{y-7}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}+6y+8}{y^{2}-5y-14}.

$$\frac{y+4}{y-7}+\frac{\left(y+2\right)\left(y+4\right)}{\left(y-7\right)\left(y+2\right)}-\frac{y^{2}-3y-28}{y^{2}-14y+49}$$

Cancel out y+2 in both numerator and denominator.

$$\frac{y+4}{y-7}+\frac{y+4}{y-7}-\frac{y^{2}-3y-28}{y^{2}-14y+49}$$

Combine \frac{y+4}{y-7} and \frac{y+4}{y-7} to get 2\times \frac{y+4}{y-7}.

$$2\times \frac{y+4}{y-7}-\frac{y^{2}-3y-28}{y^{2}-14y+49}$$

Factor the expressions that are not already factored in \frac{y^{2}-3y-28}{y^{2}-14y+49}.

$$2\times \frac{y+4}{y-7}-\frac{\left(y-7\right)\left(y+4\right)}{\left(y-7\right)^{2}}$$

Cancel out y-7 in both numerator and denominator.

$$2\times \frac{y+4}{y-7}-\frac{y+4}{y-7}$$

Express 2\times \frac{y+4}{y-7} as a single fraction.

$$\frac{2\left(y+4\right)}{y-7}-\frac{y+4}{y-7}$$

Since \frac{2\left(y+4\right)}{y-7} and \frac{y+4}{y-7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(y+4\right)-\left(y+4\right)}{y-7}$$

Do the multiplications in 2\left(y+4\right)-\left(y+4\right).

$$\frac{2y+8-y-4}{y-7}$$

Combine like terms in 2y+8-y-4.

$$\frac{y+4}{y-7}$$