Solve 4y^2-9/2y^2+9y-18+2y^2+y-3/y^2+5y-6

$$\frac { 4 y ^ { 2 } - 9 } { 2 y ^ { 2 } + 9 y - 18 } + \frac { 2 y ^ { 2 } + y - 3 } { y ^ { 2 } + 5 y - 6 }$$

Evaluate

$$\frac{2\left(2y+3\right)}{y+6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4y^{2}-9}{2y^{2}+9y-18}.

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

Cancel out 2y-3 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{2y^{2}+y-3}{y^{2}+5y-6}.

$$\frac{2y+3}{y+6}+\frac{\left(y-1\right)\left(2y+3\right)}{\left(y-1\right)\left(y+6\right)}$$

Cancel out y-1 in both numerator and denominator.

$$\frac{2y+3}{y+6}+\frac{2y+3}{y+6}$$

Combine \frac{2y+3}{y+6} and \frac{2y+3}{y+6} to get 2\times \frac{2y+3}{y+6}.

$$2\times \frac{2y+3}{y+6}$$

Express 2\times \frac{2y+3}{y+6} as a single fraction.

$$\frac{2\left(2y+3\right)}{y+6}$$

Use the distributive property to multiply 2 by 2y+3.

$$\frac{4y+6}{y+6}$$

Expand

$$\frac{2\left(2y+3\right)}{y+6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4y^{2}-9}{2y^{2}+9y-18}.

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

Cancel out 2y-3 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{2y^{2}+y-3}{y^{2}+5y-6}.

$$\frac{2y+3}{y+6}+\frac{\left(y-1\right)\left(2y+3\right)}{\left(y-1\right)\left(y+6\right)}$$

Cancel out y-1 in both numerator and denominator.

$$\frac{2y+3}{y+6}+\frac{2y+3}{y+6}$$

Combine \frac{2y+3}{y+6} and \frac{2y+3}{y+6} to get 2\times \frac{2y+3}{y+6}.

$$2\times \frac{2y+3}{y+6}$$

Express 2\times \frac{2y+3}{y+6} as a single fraction.

$$\frac{2\left(2y+3\right)}{y+6}$$

Use the distributive property to multiply 2 by 2y+3.

$$\frac{4y+6}{y+6}$$