Solve 3p^2+p-2/5p-4div3p^2-11p+6/20p^3-16p^2

$$\frac { 3 p ^ { 2 } + p - 2 } { 5 p - 4 } \div \frac { 3 p ^ { 2 } - 11 p + 6 } { 20 p ^ { 3 } - 16 p ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Divide \frac{3p^{2}+p-2}{5p-4} by \frac{3p^{2}-11p+6}{20p^{3}-16p^{2}} by multiplying \frac{3p^{2}+p-2}{5p-4} by the reciprocal of \frac{3p^{2}-11p+6}{20p^{3}-16p^{2}}.

$$\frac{\left(3p^{2}+p-2\right)\left(20p^{3}-16p^{2}\right)}{\left(5p-4\right)\left(3p^{2}-11p+6\right)}$$

Factor the expressions that are not already factored.

$$\frac{4\left(3p-2\right)\left(5p-4\right)\left(p+1\right)p^{2}}{\left(p-3\right)\left(3p-2\right)\left(5p-4\right)}$$

Cancel out \left(3p-2\right)\left(5p-4\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{4p^{3}+4p^{2}}{p-3}$$

Expand

$$\frac{4\left(p^{3}+p^{2}\right)}{p-3}$$

Short Solution Steps

Divide \frac{3p^{2}+p-2}{5p-4} by \frac{3p^{2}-11p+6}{20p^{3}-16p^{2}} by multiplying \frac{3p^{2}+p-2}{5p-4} by the reciprocal of \frac{3p^{2}-11p+6}{20p^{3}-16p^{2}}.

$$\frac{\left(3p^{2}+p-2\right)\left(20p^{3}-16p^{2}\right)}{\left(5p-4\right)\left(3p^{2}-11p+6\right)}$$

Factor the expressions that are not already factored.

$$\frac{4\left(3p-2\right)\left(5p-4\right)\left(p+1\right)p^{2}}{\left(p-3\right)\left(3p-2\right)\left(5p-4\right)}$$

Cancel out \left(3p-2\right)\left(5p-4\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{4p^{3}+4p^{2}}{p-3}$$