Solve 3(y-5)-4(y+3)/(y+3)(y-2)(y-5)

$$\frac { 3 ( y - 5 ) - 4 ( y + 3 ) } { ( y + 3 ) ( y - 2 ) ( y - 5 ) }$$

Evaluate

$$-\frac{y+27}{\left(y-5\right)\left(y-2\right)\left(y+3\right)}$$

Short Solution Steps

Use the distributive property to multiply 3 by y-5.

$$\frac{3y-15-4\left(y+3\right)}{\left(y+3\right)\left(y-2\right)\left(y-5\right)}$$

Use the distributive property to multiply -4 by y+3.

$$\frac{3y-15-4y-12}{\left(y+3\right)\left(y-2\right)\left(y-5\right)}$$

Combine 3y and -4y to get -y.

$$\frac{-y-15-12}{\left(y+3\right)\left(y-2\right)\left(y-5\right)}$$

Subtract 12 from -15 to get -27.

$$\frac{-y-27}{\left(y+3\right)\left(y-2\right)\left(y-5\right)}$$

Apply the distributive property by multiplying each term of y+3 by each term of y-2.

$$\frac{-y-27}{\left(y^{2}-2y+3y-6\right)\left(y-5\right)}$$

Combine -2y and 3y to get y.

$$\frac{-y-27}{\left(y^{2}+y-6\right)\left(y-5\right)}$$

Apply the distributive property by multiplying each term of y^{2}+y-6 by each term of y-5.

$$\frac{-y-27}{y^{3}-5y^{2}+y^{2}-5y-6y+30}$$

Combine -5y^{2} and y^{2} to get -4y^{2}.

$$\frac{-y-27}{y^{3}-4y^{2}-5y-6y+30}$$

Combine -5y and -6y to get -11y.

$$\frac{-y-27}{y^{3}-4y^{2}-11y+30}$$

Expand

$$-\frac{y+27}{\left(y-5\right)\left(y-2\right)\left(y+3\right)}$$

Short Solution Steps

Use the distributive property to multiply 3 by y-5.

$$\frac{3y-15-4\left(y+3\right)}{\left(y+3\right)\left(y-2\right)\left(y-5\right)}$$

Use the distributive property to multiply -4 by y+3.

$$\frac{3y-15-4y-12}{\left(y+3\right)\left(y-2\right)\left(y-5\right)}$$

Combine 3y and -4y to get -y.

$$\frac{-y-15-12}{\left(y+3\right)\left(y-2\right)\left(y-5\right)}$$

Subtract 12 from -15 to get -27.

$$\frac{-y-27}{\left(y+3\right)\left(y-2\right)\left(y-5\right)}$$

Apply the distributive property by multiplying each term of y+3 by each term of y-2.

$$\frac{-y-27}{\left(y^{2}-2y+3y-6\right)\left(y-5\right)}$$

Combine -2y and 3y to get y.

$$\frac{-y-27}{\left(y^{2}+y-6\right)\left(y-5\right)}$$

Apply the distributive property by multiplying each term of y^{2}+y-6 by each term of y-5.

$$\frac{-y-27}{y^{3}-5y^{2}+y^{2}-5y-6y+30}$$

Combine -5y^{2} and y^{2} to get -4y^{2}.

$$\frac{-y-27}{y^{3}-4y^{2}-5y-6y+30}$$

Combine -5y and -6y to get -11y.

$$\frac{-y-27}{y^{3}-4y^{2}-11y+30}$$