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

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

Evaluate

$$\frac{\left(y-2\right)\left(y+4\right)}{y^{2}+3y-175}$$

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}.

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

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.

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

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

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

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

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

Express 5\times \frac{-35}{y+3} as a single fraction.

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

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

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

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

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

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

$$\frac{\frac{y^{2}+2y-8}{y+3}}{\frac{y^{2}+3y-175}{y+3}}$$

Divide \frac{y^{2}+2y-8}{y+3} by \frac{y^{2}+3y-175}{y+3} by multiplying \frac{y^{2}+2y-8}{y+3} by the reciprocal of \frac{y^{2}+3y-175}{y+3}.

$$\frac{\left(y^{2}+2y-8\right)\left(y+3\right)}{\left(y+3\right)\left(y^{2}+3y-175\right)}$$

Cancel out y+3 in both numerator and denominator.

$$\frac{y^{2}+2y-8}{y^{2}+3y-175}$$

Expand

$$\frac{y^{2}+2y-8}{y^{2}+3y-175}$$

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}.

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

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.

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

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

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

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

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

Express 5\times \frac{-35}{y+3} as a single fraction.

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

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

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

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

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

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

$$\frac{\frac{y^{2}+2y-8}{y+3}}{\frac{y^{2}+3y-175}{y+3}}$$

Divide \frac{y^{2}+2y-8}{y+3} by \frac{y^{2}+3y-175}{y+3} by multiplying \frac{y^{2}+2y-8}{y+3} by the reciprocal of \frac{y^{2}+3y-175}{y+3}.

$$\frac{\left(y^{2}+2y-8\right)\left(y+3\right)}{\left(y+3\right)\left(y^{2}+3y-175\right)}$$

Cancel out y+3 in both numerator and denominator.

$$\frac{y^{2}+2y-8}{y^{2}+3y-175}$$