Solve 7r^2+51r-40/42-r-72div49r^2-21r-10/7r+2

$$\frac { 7 r ^ { 2 } + 51 r - 40 } { 42 - r - 72 } \div \frac { 49 r ^ { 2 } - 21 r - 10 } { 7 r + 2 }$$

Evaluate

$$-\frac{r+8}{r+30}$$

Short Solution Steps

Divide \frac{7r^{2}+51r-40}{42-r-72} by \frac{49r^{2}-21r-10}{7r+2} by multiplying \frac{7r^{2}+51r-40}{42-r-72} by the reciprocal of \frac{49r^{2}-21r-10}{7r+2}.

$$\frac{\left(7r^{2}+51r-40\right)\left(7r+2\right)}{\left(42-r-72\right)\left(49r^{2}-21r-10\right)}$$

Subtract 72 from 42 to get -30.

$$\frac{\left(7r^{2}+51r-40\right)\left(7r+2\right)}{\left(-30-r\right)\left(49r^{2}-21r-10\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(7r-5\right)\left(r+8\right)\left(7r+2\right)}{\left(-r-30\right)\left(7r-5\right)\left(7r+2\right)}$$

Cancel out \left(7r-5\right)\left(7r+2\right) in both numerator and denominator.

$$\frac{r+8}{-r-30}$$

Expand

$$-\frac{r+8}{r+30}$$

Short Solution Steps

Divide \frac{7r^{2}+51r-40}{42-r-72} by \frac{49r^{2}-21r-10}{7r+2} by multiplying \frac{7r^{2}+51r-40}{42-r-72} by the reciprocal of \frac{49r^{2}-21r-10}{7r+2}.

$$\frac{\left(7r^{2}+51r-40\right)\left(7r+2\right)}{\left(42-r-72\right)\left(49r^{2}-21r-10\right)}$$

Subtract 72 from 42 to get -30.

$$\frac{\left(7r^{2}+51r-40\right)\left(7r+2\right)}{\left(-30-r\right)\left(49r^{2}-21r-10\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(7r-5\right)\left(r+8\right)\left(7r+2\right)}{\left(-r-30\right)\left(7r-5\right)\left(7r+2\right)}$$

Cancel out \left(7r-5\right)\left(7r+2\right) in both numerator and denominator.

$$\frac{r+8}{-r-30}$$