Solve 3y^2+12y-135/y^2-11y+30div3y^2+34y+63/6y^2-22y-84

$$\frac { 3 y ^ { 2 } + 12 y - 135 } { y ^ { 2 } - 11 y + 30 } \div \frac { 3 y ^ { 2 } + 34 y + 63 } { 6 y ^ { 2 } - 22 y - 84 }$$

Evaluate

$$6$$

Short Solution Steps

Divide \frac{3y^{2}+12y-135}{y^{2}-11y+30} by \frac{3y^{2}+34y+63}{6y^{2}-22y-84} by multiplying \frac{3y^{2}+12y-135}{y^{2}-11y+30} by the reciprocal of \frac{3y^{2}+34y+63}{6y^{2}-22y-84}.

$$\frac{\left(3y^{2}+12y-135\right)\left(6y^{2}-22y-84\right)}{\left(y^{2}-11y+30\right)\left(3y^{2}+34y+63\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\times 3\left(y-6\right)\left(y-5\right)\left(y+9\right)\left(3y+7\right)}{\left(y-6\right)\left(y-5\right)\left(y+9\right)\left(3y+7\right)}$$

Cancel out \left(y-6\right)\left(y-5\right)\left(y+9\right)\left(3y+7\right) in both numerator and denominator.

$$2\times 3$$

Multiply 2 and 3 to get 6.

$$6$$

Factor

$$2\times 3$$