Solve frac{2x^{2}-x-1}{y^{2}-3y+2}*y^2+9y-22/2x^2-x-1div4x^2-4x-3/6x^2+5x+1

$$\frac { 2 x ^ { 2 } - x - 1 } { y ^ { 2 } - 3 y + 2 } \cdot \frac { y ^ { 2 } + 9 y - 22 } { 2 x ^ { 2 } - x - 1 } \div \frac { 4 x ^ { 2 } - 4 x - 3 } { 6 x ^ { 2 } + 5 x + 1 }$$

Evaluate

$$\frac{\left(y+11\right)\left(3x+1\right)}{\left(y-1\right)\left(2x-3\right)}$$

Short Solution Steps

Multiply \frac{2x^{2}-x-1}{y^{2}-3y+2} times \frac{y^{2}+9y-22}{2x^{2}-x-1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(2x^{2}-x-1\right)\left(y^{2}+9y-22\right)}{\left(y^{2}-3y+2\right)\left(2x^{2}-x-1\right)}}{\frac{4x^{2}-4x-3}{6x^{2}+5x+1}}$$

Cancel out 2x^{2}-x-1 in both numerator and denominator.

$$\frac{\frac{y^{2}+9y-22}{y^{2}-3y+2}}{\frac{4x^{2}-4x-3}{6x^{2}+5x+1}}$$

Factor the expressions that are not already factored in \frac{4x^{2}-4x-3}{6x^{2}+5x+1}.

$$\frac{\frac{y^{2}+9y-22}{y^{2}-3y+2}}{\frac{\left(2x-3\right)\left(2x+1\right)}{\left(2x+1\right)\left(3x+1\right)}}$$

Cancel out 2x+1 in both numerator and denominator.

$$\frac{\frac{y^{2}+9y-22}{y^{2}-3y+2}}{\frac{2x-3}{3x+1}}$$

Divide \frac{y^{2}+9y-22}{y^{2}-3y+2} by \frac{2x-3}{3x+1} by multiplying \frac{y^{2}+9y-22}{y^{2}-3y+2} by the reciprocal of \frac{2x-3}{3x+1}.

$$\frac{\left(y^{2}+9y-22\right)\left(3x+1\right)}{\left(y^{2}-3y+2\right)\left(2x-3\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-2\right)\left(y+11\right)\left(3x+1\right)}{\left(y-2\right)\left(y-1\right)\left(2x-3\right)}$$

Cancel out y-2 in both numerator and denominator.

$$\frac{\left(y+11\right)\left(3x+1\right)}{\left(y-1\right)\left(2x-3\right)}$$

Expand the expression.

$$\frac{3xy+33x+y+11}{2xy-2x-3y+3}$$

Expand

$$\frac{3xy+33x+y+11}{\left(y-1\right)\left(2x-3\right)}$$

Short Solution Steps

Multiply \frac{2x^{2}-x-1}{y^{2}-3y+2} times \frac{y^{2}+9y-22}{2x^{2}-x-1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(2x^{2}-x-1\right)\left(y^{2}+9y-22\right)}{\left(y^{2}-3y+2\right)\left(2x^{2}-x-1\right)}}{\frac{4x^{2}-4x-3}{6x^{2}+5x+1}}$$

Cancel out 2x^{2}-x-1 in both numerator and denominator.

$$\frac{\frac{y^{2}+9y-22}{y^{2}-3y+2}}{\frac{4x^{2}-4x-3}{6x^{2}+5x+1}}$$

Factor the expressions that are not already factored in \frac{4x^{2}-4x-3}{6x^{2}+5x+1}.

$$\frac{\frac{y^{2}+9y-22}{y^{2}-3y+2}}{\frac{\left(2x-3\right)\left(2x+1\right)}{\left(2x+1\right)\left(3x+1\right)}}$$

Cancel out 2x+1 in both numerator and denominator.

$$\frac{\frac{y^{2}+9y-22}{y^{2}-3y+2}}{\frac{2x-3}{3x+1}}$$

Divide \frac{y^{2}+9y-22}{y^{2}-3y+2} by \frac{2x-3}{3x+1} by multiplying \frac{y^{2}+9y-22}{y^{2}-3y+2} by the reciprocal of \frac{2x-3}{3x+1}.

$$\frac{\left(y^{2}+9y-22\right)\left(3x+1\right)}{\left(y^{2}-3y+2\right)\left(2x-3\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-2\right)\left(y+11\right)\left(3x+1\right)}{\left(y-2\right)\left(y-1\right)\left(2x-3\right)}$$

Cancel out y-2 in both numerator and denominator.

$$\frac{\left(y+11\right)\left(3x+1\right)}{\left(y-1\right)\left(2x-3\right)}$$

Expand the expression.

$$\frac{3xy+33x+y+11}{2xy-2x-3y+3}$$