Solve 8t^3+27/9-4t^2div4t^2-6t+9/2t^2-t-3

$$\frac { 8 t ^ { 3 } + 27 } { 9 - 4 t ^ { 2 } } \div \frac { 4 t ^ { 2 } - 6 t + 9 } { 2 t ^ { 2 } - t - 3 }$$

Evaluate

$$-\left(t+1\right)$$

Short Solution Steps

Divide \frac{8t^{3}+27}{9-4t^{2}} by \frac{4t^{2}-6t+9}{2t^{2}-t-3} by multiplying \frac{8t^{3}+27}{9-4t^{2}} by the reciprocal of \frac{4t^{2}-6t+9}{2t^{2}-t-3}.

$$\frac{\left(8t^{3}+27\right)\left(2t^{2}-t-3\right)}{\left(9-4t^{2}\right)\left(4t^{2}-6t+9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(2t-3\right)\left(t+1\right)\left(2t+3\right)\left(4t^{2}-6t+9\right)}{\left(-2t-3\right)\left(2t-3\right)\left(4t^{2}-6t+9\right)}$$

Extract the negative sign in 3+2t.

$$\frac{-\left(-2t-3\right)\left(2t-3\right)\left(t+1\right)\left(4t^{2}-6t+9\right)}{\left(-2t-3\right)\left(2t-3\right)\left(4t^{2}-6t+9\right)}$$

Cancel out \left(-2t-3\right)\left(2t-3\right)\left(4t^{2}-6t+9\right) in both numerator and denominator.

$$-\left(t+1\right)$$

Expand the expression.

$$-t-1$$

Expand

$$-t-1$$

Short Solution Steps

Divide \frac{8t^{3}+27}{9-4t^{2}} by \frac{4t^{2}-6t+9}{2t^{2}-t-3} by multiplying \frac{8t^{3}+27}{9-4t^{2}} by the reciprocal of \frac{4t^{2}-6t+9}{2t^{2}-t-3}.

$$\frac{\left(8t^{3}+27\right)\left(2t^{2}-t-3\right)}{\left(9-4t^{2}\right)\left(4t^{2}-6t+9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(2t-3\right)\left(t+1\right)\left(2t+3\right)\left(4t^{2}-6t+9\right)}{\left(-2t-3\right)\left(2t-3\right)\left(4t^{2}-6t+9\right)}$$

Extract the negative sign in 3+2t.

$$\frac{-\left(-2t-3\right)\left(2t-3\right)\left(t+1\right)\left(4t^{2}-6t+9\right)}{\left(-2t-3\right)\left(2t-3\right)\left(4t^{2}-6t+9\right)}$$

Cancel out \left(-2t-3\right)\left(2t-3\right)\left(4t^{2}-6t+9\right) in both numerator and denominator.

$$-\left(t+1\right)$$

Expand the expression.

$$-t-1$$