Solve y-1-5/y+3/y+5-frac{35{y+3}}

$$\frac{ y-1- \frac{ 5 }{ y+3 } }{ y+5- \frac{ 35 }{ y+3 } }$$

Evaluate

$$\frac{y+4}{y+10}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply y-1 times \frac{y+3}{y+3}.

$$\frac{\frac{\left(y-1\right)\left(y+3\right)}{y+3}-\frac{5}{y+3}}{y+5-\frac{35}{y+3}}$$

Since \frac{\left(y-1\right)\left(y+3\right)}{y+3} and \frac{5}{y+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(y-1\right)\left(y+3\right)-5}{y+3}}{y+5-\frac{35}{y+3}}$$

Do the multiplications in \left(y-1\right)\left(y+3\right)-5.

$$\frac{\frac{y^{2}+3y-y-3-5}{y+3}}{y+5-\frac{35}{y+3}}$$

Combine like terms in y^{2}+3y-y-3-5.

$$\frac{\frac{y^{2}+2y-8}{y+3}}{y+5-\frac{35}{y+3}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y+5 times \frac{y+3}{y+3}.

$$\frac{\frac{y^{2}+2y-8}{y+3}}{\frac{\left(y+5\right)\left(y+3\right)}{y+3}-\frac{35}{y+3}}$$

Since \frac{\left(y+5\right)\left(y+3\right)}{y+3} and \frac{35}{y+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{y^{2}+2y-8}{y+3}}{\frac{\left(y+5\right)\left(y+3\right)-35}{y+3}}$$

Do the multiplications in \left(y+5\right)\left(y+3\right)-35.

$$\frac{\frac{y^{2}+2y-8}{y+3}}{\frac{y^{2}+3y+5y+15-35}{y+3}}$$

Combine like terms in y^{2}+3y+5y+15-35.

$$\frac{\frac{y^{2}+2y-8}{y+3}}{\frac{y^{2}+8y-20}{y+3}}$$

Divide \frac{y^{2}+2y-8}{y+3} by \frac{y^{2}+8y-20}{y+3} by multiplying \frac{y^{2}+2y-8}{y+3} by the reciprocal of \frac{y^{2}+8y-20}{y+3}.

$$\frac{\left(y^{2}+2y-8\right)\left(y+3\right)}{\left(y+3\right)\left(y^{2}+8y-20\right)}$$

Cancel out y+3 in both numerator and denominator.

$$\frac{y^{2}+2y-8}{y^{2}+8y-20}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-2\right)\left(y+4\right)}{\left(y-2\right)\left(y+10\right)}$$

Cancel out y-2 in both numerator and denominator.

$$\frac{y+4}{y+10}$$

Expand

$$\frac{y+4}{y+10}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply y-1 times \frac{y+3}{y+3}.

$$\frac{\frac{\left(y-1\right)\left(y+3\right)}{y+3}-\frac{5}{y+3}}{y+5-\frac{35}{y+3}}$$

Since \frac{\left(y-1\right)\left(y+3\right)}{y+3} and \frac{5}{y+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(y-1\right)\left(y+3\right)-5}{y+3}}{y+5-\frac{35}{y+3}}$$

Do the multiplications in \left(y-1\right)\left(y+3\right)-5.

$$\frac{\frac{y^{2}+3y-y-3-5}{y+3}}{y+5-\frac{35}{y+3}}$$

Combine like terms in y^{2}+3y-y-3-5.

$$\frac{\frac{y^{2}+2y-8}{y+3}}{y+5-\frac{35}{y+3}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y+5 times \frac{y+3}{y+3}.

$$\frac{\frac{y^{2}+2y-8}{y+3}}{\frac{\left(y+5\right)\left(y+3\right)}{y+3}-\frac{35}{y+3}}$$

Since \frac{\left(y+5\right)\left(y+3\right)}{y+3} and \frac{35}{y+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{y^{2}+2y-8}{y+3}}{\frac{\left(y+5\right)\left(y+3\right)-35}{y+3}}$$

Do the multiplications in \left(y+5\right)\left(y+3\right)-35.

$$\frac{\frac{y^{2}+2y-8}{y+3}}{\frac{y^{2}+3y+5y+15-35}{y+3}}$$

Combine like terms in y^{2}+3y+5y+15-35.

$$\frac{\frac{y^{2}+2y-8}{y+3}}{\frac{y^{2}+8y-20}{y+3}}$$

Divide \frac{y^{2}+2y-8}{y+3} by \frac{y^{2}+8y-20}{y+3} by multiplying \frac{y^{2}+2y-8}{y+3} by the reciprocal of \frac{y^{2}+8y-20}{y+3}.

$$\frac{\left(y^{2}+2y-8\right)\left(y+3\right)}{\left(y+3\right)\left(y^{2}+8y-20\right)}$$

Cancel out y+3 in both numerator and denominator.

$$\frac{y^{2}+2y-8}{y^{2}+8y-20}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-2\right)\left(y+4\right)}{\left(y-2\right)\left(y+10\right)}$$

Cancel out y-2 in both numerator and denominator.

$$\frac{y+4}{y+10}$$