Solve (t+2)(t+3)/(t+4)(t-2)*(t+4)(t+7)/(t+2)(t+3)

$$\frac { ( t + 2 ) ( t + 3 ) } { ( t + 4 ) ( t - 2 ) } \cdot \frac { ( t + 4 ) ( t + 7 ) } { ( t + 2 ) ( t + 3 ) }$$

Evaluate

$$\frac{t+7}{t-2}$$

Short Solution Steps

Apply the distributive property by multiplying each term of t+2 by each term of t+3.

$$\frac{t^{2}+3t+2t+6}{\left(t+4\right)\left(t-2\right)}\times \frac{\left(t+4\right)\left(t+7\right)}{\left(t+2\right)\left(t+3\right)}$$

Combine 3t and 2t to get 5t.

$$\frac{t^{2}+5t+6}{\left(t+4\right)\left(t-2\right)}\times \frac{\left(t+4\right)\left(t+7\right)}{\left(t+2\right)\left(t+3\right)}$$

Apply the distributive property by multiplying each term of t+4 by each term of t-2.

$$\frac{t^{2}+5t+6}{t^{2}-2t+4t-8}\times \frac{\left(t+4\right)\left(t+7\right)}{\left(t+2\right)\left(t+3\right)}$$

Combine -2t and 4t to get 2t.

$$\frac{t^{2}+5t+6}{t^{2}+2t-8}\times \frac{\left(t+4\right)\left(t+7\right)}{\left(t+2\right)\left(t+3\right)}$$

Apply the distributive property by multiplying each term of t+4 by each term of t+7.

$$\frac{t^{2}+5t+6}{t^{2}+2t-8}\times \frac{t^{2}+7t+4t+28}{\left(t+2\right)\left(t+3\right)}$$

Combine 7t and 4t to get 11t.

$$\frac{t^{2}+5t+6}{t^{2}+2t-8}\times \frac{t^{2}+11t+28}{\left(t+2\right)\left(t+3\right)}$$

Apply the distributive property by multiplying each term of t+2 by each term of t+3.

$$\frac{t^{2}+5t+6}{t^{2}+2t-8}\times \frac{t^{2}+11t+28}{t^{2}+3t+2t+6}$$

Combine 3t and 2t to get 5t.

$$\frac{t^{2}+5t+6}{t^{2}+2t-8}\times \frac{t^{2}+11t+28}{t^{2}+5t+6}$$

Multiply \frac{t^{2}+5t+6}{t^{2}+2t-8} times \frac{t^{2}+11t+28}{t^{2}+5t+6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(t^{2}+5t+6\right)\left(t^{2}+11t+28\right)}{\left(t^{2}+2t-8\right)\left(t^{2}+5t+6\right)}$$

Cancel out t^{2}+5t+6 in both numerator and denominator.

$$\frac{t^{2}+11t+28}{t^{2}+2t-8}$$

Factor the expressions that are not already factored.

$$\frac{\left(t+4\right)\left(t+7\right)}{\left(t-2\right)\left(t+4\right)}$$

Cancel out t+4 in both numerator and denominator.

$$\frac{t+7}{t-2}$$

Expand

$$\frac{t+7}{t-2}$$

Short Solution Steps

Apply the distributive property by multiplying each term of t+2 by each term of t+3.

$$\frac{t^{2}+3t+2t+6}{\left(t+4\right)\left(t-2\right)}\times \frac{\left(t+4\right)\left(t+7\right)}{\left(t+2\right)\left(t+3\right)}$$

Combine 3t and 2t to get 5t.

$$\frac{t^{2}+5t+6}{\left(t+4\right)\left(t-2\right)}\times \frac{\left(t+4\right)\left(t+7\right)}{\left(t+2\right)\left(t+3\right)}$$

Apply the distributive property by multiplying each term of t+4 by each term of t-2.

$$\frac{t^{2}+5t+6}{t^{2}-2t+4t-8}\times \frac{\left(t+4\right)\left(t+7\right)}{\left(t+2\right)\left(t+3\right)}$$

Combine -2t and 4t to get 2t.

$$\frac{t^{2}+5t+6}{t^{2}+2t-8}\times \frac{\left(t+4\right)\left(t+7\right)}{\left(t+2\right)\left(t+3\right)}$$

Apply the distributive property by multiplying each term of t+4 by each term of t+7.

$$\frac{t^{2}+5t+6}{t^{2}+2t-8}\times \frac{t^{2}+7t+4t+28}{\left(t+2\right)\left(t+3\right)}$$

Combine 7t and 4t to get 11t.

$$\frac{t^{2}+5t+6}{t^{2}+2t-8}\times \frac{t^{2}+11t+28}{\left(t+2\right)\left(t+3\right)}$$

Apply the distributive property by multiplying each term of t+2 by each term of t+3.

$$\frac{t^{2}+5t+6}{t^{2}+2t-8}\times \frac{t^{2}+11t+28}{t^{2}+3t+2t+6}$$

Combine 3t and 2t to get 5t.

$$\frac{t^{2}+5t+6}{t^{2}+2t-8}\times \frac{t^{2}+11t+28}{t^{2}+5t+6}$$

Multiply \frac{t^{2}+5t+6}{t^{2}+2t-8} times \frac{t^{2}+11t+28}{t^{2}+5t+6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(t^{2}+5t+6\right)\left(t^{2}+11t+28\right)}{\left(t^{2}+2t-8\right)\left(t^{2}+5t+6\right)}$$

Cancel out t^{2}+5t+6 in both numerator and denominator.

$$\frac{t^{2}+11t+28}{t^{2}+2t-8}$$

Factor the expressions that are not already factored.

$$\frac{\left(t+4\right)\left(t+7\right)}{\left(t-2\right)\left(t+4\right)}$$

Cancel out t+4 in both numerator and denominator.

$$\frac{t+7}{t-2}$$