Solve t^2+5t-24/t^2+6t-27*t^2-8t-9/t^2+9t+8

$$\frac { t ^ { 2 } + 5 t - 24 } { t ^ { 2 } + 6 t - 27 } \cdot \frac { t ^ { 2 } - 8 t - 9 } { t ^ { 2 } + 9 t + 8 }$$

Evaluate

$$\frac{t-9}{t+9}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{t^{2}+5t-24}{t^{2}+6t-27}.

$$\frac{\left(t-3\right)\left(t+8\right)}{\left(t-3\right)\left(t+9\right)}\times \frac{t^{2}-8t-9}{t^{2}+9t+8}$$

Cancel out t-3 in both numerator and denominator.

$$\frac{t+8}{t+9}\times \frac{t^{2}-8t-9}{t^{2}+9t+8}$$

Factor the expressions that are not already factored in \frac{t^{2}-8t-9}{t^{2}+9t+8}.

$$\frac{t+8}{t+9}\times \frac{\left(t-9\right)\left(t+1\right)}{\left(t+1\right)\left(t+8\right)}$$

Cancel out t+1 in both numerator and denominator.

$$\frac{t+8}{t+9}\times \frac{t-9}{t+8}$$

Multiply \frac{t+8}{t+9} times \frac{t-9}{t+8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(t+8\right)\left(t-9\right)}{\left(t+9\right)\left(t+8\right)}$$

Cancel out t+8 in both numerator and denominator.

$$\frac{t-9}{t+9}$$

Expand

$$\frac{t-9}{t+9}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{t^{2}+5t-24}{t^{2}+6t-27}.

$$\frac{\left(t-3\right)\left(t+8\right)}{\left(t-3\right)\left(t+9\right)}\times \frac{t^{2}-8t-9}{t^{2}+9t+8}$$

Cancel out t-3 in both numerator and denominator.

$$\frac{t+8}{t+9}\times \frac{t^{2}-8t-9}{t^{2}+9t+8}$$

Factor the expressions that are not already factored in \frac{t^{2}-8t-9}{t^{2}+9t+8}.

$$\frac{t+8}{t+9}\times \frac{\left(t-9\right)\left(t+1\right)}{\left(t+1\right)\left(t+8\right)}$$

Cancel out t+1 in both numerator and denominator.

$$\frac{t+8}{t+9}\times \frac{t-9}{t+8}$$

Multiply \frac{t+8}{t+9} times \frac{t-9}{t+8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(t+8\right)\left(t-9\right)}{\left(t+9\right)\left(t+8\right)}$$

Cancel out t+8 in both numerator and denominator.

$$\frac{t-9}{t+9}$$