Solve 7r^2-33r+20/15r^2+10r-5/frac{28r-20{15r^2+10r-5}}

$$\frac { \frac { 7 r ^ { 2 } - 33 r + 20 } { 15 r ^ { 2 } + 10 r - 5 } } { \frac { 28 r - 20 } { 15 r ^ { 2 } + 10 r - 5 } }$$

Evaluate

$$\frac{r}{4}-1$$

Short Solution Steps

Divide \frac{7r^{2}-33r+20}{15r^{2}+10r-5} by \frac{28r-20}{15r^{2}+10r-5} by multiplying \frac{7r^{2}-33r+20}{15r^{2}+10r-5} by the reciprocal of \frac{28r-20}{15r^{2}+10r-5}.

$$\frac{\left(7r^{2}-33r+20\right)\left(15r^{2}+10r-5\right)}{\left(15r^{2}+10r-5\right)\left(28r-20\right)}$$

Cancel out 15r^{2}+10r-5 in both numerator and denominator.

$$\frac{7r^{2}-33r+20}{28r-20}$$

Factor the expressions that are not already factored.

$$\frac{\left(r-4\right)\left(7r-5\right)}{4\left(7r-5\right)}$$

Cancel out 7r-5 in both numerator and denominator.

$$\frac{r-4}{4}$$

Expand

$$\frac{r}{4}-1$$

Short Solution Steps

Divide \frac{7r^{2}-33r+20}{15r^{2}+10r-5} by \frac{28r-20}{15r^{2}+10r-5} by multiplying \frac{7r^{2}-33r+20}{15r^{2}+10r-5} by the reciprocal of \frac{28r-20}{15r^{2}+10r-5}.

$$\frac{\left(7r^{2}-33r+20\right)\left(15r^{2}+10r-5\right)}{\left(15r^{2}+10r-5\right)\left(28r-20\right)}$$

Cancel out 15r^{2}+10r-5 in both numerator and denominator.

$$\frac{7r^{2}-33r+20}{28r-20}$$

Factor the expressions that are not already factored.

$$\frac{\left(r-4\right)\left(7r-5\right)}{4\left(7r-5\right)}$$

Cancel out 7r-5 in both numerator and denominator.

$$\frac{r-4}{4}$$