Solve 4y^2-9/2y^2+9y-18div2y^2+y-3/y^2+5y-6

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

Evaluate

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Short Solution Steps

Divide \frac{4y^{2}-9}{2y^{2}+9y-18} by \frac{2y^{2}+y-3}{y^{2}+5y-6} by multiplying \frac{4y^{2}-9}{2y^{2}+9y-18} by the reciprocal of \frac{2y^{2}+y-3}{y^{2}+5y-6}.

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

Factor the expressions that are not already factored.

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

Cancel out \left(y-1\right)\left(2y-3\right)\left(y+6\right)\left(2y+3\right) in both numerator and denominator.

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Factor

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