Solve t^2+8t+15/t^2+2t+1divt^2+7t+10/t^2+3t+2

$$\frac { t ^ { 2 } + 8 t + 15 } { t ^ { 2 } + 2 t + 1 } \div \frac { t ^ { 2 } + 7 t + 10 } { t ^ { 2 } + 3 t + 2 }$$

Evaluate

$$\frac{t+3}{t+1}$$

Short Solution Steps

Divide \frac{t^{2}+8t+15}{t^{2}+2t+1} by \frac{t^{2}+7t+10}{t^{2}+3t+2} by multiplying \frac{t^{2}+8t+15}{t^{2}+2t+1} by the reciprocal of \frac{t^{2}+7t+10}{t^{2}+3t+2}.

$$\frac{\left(t^{2}+8t+15\right)\left(t^{2}+3t+2\right)}{\left(t^{2}+2t+1\right)\left(t^{2}+7t+10\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(t+1\right)\left(t+2\right)\left(t+3\right)\left(t+5\right)}{\left(t+2\right)\left(t+5\right)\left(t+1\right)^{2}}$$

Cancel out \left(t+1\right)\left(t+2\right)\left(t+5\right) in both numerator and denominator.

$$\frac{t+3}{t+1}$$

Expand

$$\frac{t+3}{t+1}$$

Short Solution Steps

Divide \frac{t^{2}+8t+15}{t^{2}+2t+1} by \frac{t^{2}+7t+10}{t^{2}+3t+2} by multiplying \frac{t^{2}+8t+15}{t^{2}+2t+1} by the reciprocal of \frac{t^{2}+7t+10}{t^{2}+3t+2}.

$$\frac{\left(t^{2}+8t+15\right)\left(t^{2}+3t+2\right)}{\left(t^{2}+2t+1\right)\left(t^{2}+7t+10\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(t+1\right)\left(t+2\right)\left(t+3\right)\left(t+5\right)}{\left(t+2\right)\left(t+5\right)\left(t+1\right)^{2}}$$

Cancel out \left(t+1\right)\left(t+2\right)\left(t+5\right) in both numerator and denominator.

$$\frac{t+3}{t+1}$$