Solve t^2-25/4t+20div2t^2-20t+50/8t+40

$$\frac { t ^ { 2 } - 25 } { 4 t + 20 } \div \frac { 2 t ^ { 2 } - 20 t + 50 } { 8 t + 40 }$$

Evaluate

$$\frac{t+5}{t-5}$$

Short Solution Steps

Divide \frac{t^{2}-25}{4t+20} by \frac{2t^{2}-20t+50}{8t+40} by multiplying \frac{t^{2}-25}{4t+20} by the reciprocal of \frac{2t^{2}-20t+50}{8t+40}.

$$\frac{\left(t^{2}-25\right)\left(8t+40\right)}{\left(4t+20\right)\left(2t^{2}-20t+50\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(t-5\right)\left(t+5\right)^{2}}{2\times 4\left(t+5\right)\left(t-5\right)^{2}}$$

Cancel out 2\times 4\left(t-5\right)\left(t+5\right) in both numerator and denominator.

$$\frac{t+5}{t-5}$$

Expand

$$\frac{t+5}{t-5}$$

Short Solution Steps

Divide \frac{t^{2}-25}{4t+20} by \frac{2t^{2}-20t+50}{8t+40} by multiplying \frac{t^{2}-25}{4t+20} by the reciprocal of \frac{2t^{2}-20t+50}{8t+40}.

$$\frac{\left(t^{2}-25\right)\left(8t+40\right)}{\left(4t+20\right)\left(2t^{2}-20t+50\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(t-5\right)\left(t+5\right)^{2}}{2\times 4\left(t+5\right)\left(t-5\right)^{2}}$$

Cancel out 2\times 4\left(t-5\right)\left(t+5\right) in both numerator and denominator.

$$\frac{t+5}{t-5}$$