Solve 2t^2-5t-12/3t^2-4t-7*3t^2+11t-42/t^2+2t-24

$$\frac { 2 t ^ { 2 } - 5 t - 12 } { 3 t ^ { 2 } - 4 t - 7 } \cdot \frac { 3 t ^ { 2 } + 11 t - 42 } { t ^ { 2 } + 2 t - 24 }$$

Evaluate

$$\frac{2t+3}{t+1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3t^{2}+11t-42}{t^{2}+2t-24}.

$$\frac{2t^{2}-5t-12}{3t^{2}-4t-7}\times \frac{\left(3t-7\right)\left(t+6\right)}{\left(t-4\right)\left(t+6\right)}$$

Cancel out t+6 in both numerator and denominator.

$$\frac{2t^{2}-5t-12}{3t^{2}-4t-7}\times \frac{3t-7}{t-4}$$

Multiply \frac{2t^{2}-5t-12}{3t^{2}-4t-7} times \frac{3t-7}{t-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2t^{2}-5t-12\right)\left(3t-7\right)}{\left(3t^{2}-4t-7\right)\left(t-4\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(t-4\right)\left(3t-7\right)\left(2t+3\right)}{\left(t-4\right)\left(3t-7\right)\left(t+1\right)}$$

Cancel out \left(t-4\right)\left(3t-7\right) in both numerator and denominator.

$$\frac{2t+3}{t+1}$$

Expand

$$\frac{2t+3}{t+1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3t^{2}+11t-42}{t^{2}+2t-24}.

$$\frac{2t^{2}-5t-12}{3t^{2}-4t-7}\times \frac{\left(3t-7\right)\left(t+6\right)}{\left(t-4\right)\left(t+6\right)}$$

Cancel out t+6 in both numerator and denominator.

$$\frac{2t^{2}-5t-12}{3t^{2}-4t-7}\times \frac{3t-7}{t-4}$$

Multiply \frac{2t^{2}-5t-12}{3t^{2}-4t-7} times \frac{3t-7}{t-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2t^{2}-5t-12\right)\left(3t-7\right)}{\left(3t^{2}-4t-7\right)\left(t-4\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(t-4\right)\left(3t-7\right)\left(2t+3\right)}{\left(t-4\right)\left(3t-7\right)\left(t+1\right)}$$

Cancel out \left(t-4\right)\left(3t-7\right) in both numerator and denominator.

$$\frac{2t+3}{t+1}$$